Hybrid reactor using electrical and magnetic fields

ABSTRACT

Methods, apparatuses, devices, and systems for producing and controlling and fusion activities of nuclei. Hydrogen atoms or other neutral species (neutrals) are induced to rotational motion in a confinement region as a result of ion-neutral coupling, in which ions are driven by electric and magnetic fields. The controlled fusion activities cover a spectrum of reactions including aneutronic reactions such as proton-boron-11 fusion reactions.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. provisional application Ser. No.62/505,488, filed May 12, 2017, which is incorporated herein byreference in its entirety and for all purposes; this application is alsoa continuation in part of U.S. patent application Ser. No. 15/589,902,filed May 8, 2017, entitled REACTOR USING ELECTRICAL AND MAGNETICFIELDS; this application is also a continuation in part of U.S. patentapplication Ser. No. 15/589,913, filed May 8, 2017, entitled REACTORUSING ELECTRICAL AND MAGNETIC FIELDS; this application is also acontinuation in part of U.S. patent application Ser. No. 15/679,094,filed Aug. 16, 2017, entitled REACTOR USING ELECTRICAL AND MAGNETICFIELDS, which is a continuation of U.S. patent application Ser. No.15/589,886, filed May 8, 2017, entitled REACTOR USING ELECTRICAL ANDMAGNETIC FIELDS; this application is also a continuation in part of U.S.patent application Ser. No. 15/679,091, filed Aug. 16, 2017, entitledREACTOR USING AZIMUTHALLY VARYING ELECTRICAL FIELDS, which is acontinuation of U.S. patent application Ser. No. 15/589,905, filed May8, 2017, entitled REACTOR USING AZIMUTHALLY VARYING ELECTRICAL FIELDS;the entire disclosures of each of these priority applications areincorporated herein by reference for all purposes.

STATEMENT OF JOINT RESEARCH AGREEMENT

The subject matter and the claimed invention were made by or on behalfof Alpha Ring International, Ltd. of Monterey, Calif. and Nonlinear IonDynamics, LLC of Monterey, Calif., under a joint research agreementtitled “JOINT RESEARCH AND DEVELOPMENT AGREEMENT.” The subject matterdisclosed was developed and the claimed invention was made by, or onbehalf of, one or more parties to the joint research agreement that wasin effect on or before the effective filing date of the claimedinvention, and some aspects of the claimed invention were made as aresult of activities undertaken within the scope of the joint researchagreement.

FIELD OF THE INVENTION

The present disclosure relates to inter-nuclear reactions and reactorsfor initiating and maintaining these reactions.

BACKGROUND

Since the 1950s, the science and technology communities have beenstriving to achieve controlled and economically viable fusion. Fusion isan appealing energy source for many reasons, but after billions ofdollars and decades of research, to most, the idea of a sustainablefusion source for clean energy has become a pipe dream. The challengehas been to find a way to sustain a fusion reaction in a way that iseconomical, safe, reliable, and environmentally sound. This challengehas proved to be extraordinarily difficult. The commonly held belief inthe art is that another 25-50 years of research remain before fusion isa viable option for power generation—“As the old joke has it, fusion isthe power of the future—and always will be” (“Next ITERation?”, Sep. 3,2011, The Economist).

Prior efforts in large-scale fusion research have primarily focused ontwo methods of creating conditions for fusion ignition: inertialconfinement fusion (ICF) and magnetic confinement fusion. ICF attemptsto initiate a fusion reaction by compressing and heating fusionreactants such as a mixture of deuterium and tritium in the form of asmall pellet about the size of a pinhead. The fuel is energized bydelivering high-energy beams of laser light, electrons, or ions to thefuel target, causing the heated outer layer of the target fuel toexplode and produce shockwaves that travel inward through the fuelpellet compressing and heating the fusion reactants, thereby initiatinga fusion reaction.

At the time of this filing, the most successful ICF program is theNational Ignition Facility (NIF) which was constructed at the cost ofnearly 3.5 billion dollars and completed in 2009. NIF reached amilestone by causing a fuel pellet to give off more energy than wasapplied to it, but as of 2015, the NIF experiments were only able toreach about ⅓ of the energy levels needed for ignition. Regarding asustainable reaction, the longest reported ICF fusion reaction was onthe order of 150 picoseconds. Even if ICF efforts achieve ignitionconditions, there are still many obstacles to making it a viable energysource. For example, solutions are needed to remove heat from thereaction chamber without interfering with the fuel targets and driverbeams, and solutions are needed to mitigate the short lifetime of fusionplants due to the radioactive byproducts of the fusion reactants:deuterium and tritium reactions produce neutrons.

The second major research direction, magnetic confinement fusion,attempts to induce fusion by using magnetic fields to confine hot fusionfuel in the form of a plasma. This method seeks to lengthen the timethat ions spend close together and increase the likelihood that theyfuse. Magnetic fusion devices apply a magnetic force on chargedparticles in a manner that, when balanced with centripetal force, causesthe particles to move in circular or helical path within the plasma. Themagnetic confinement prevents the hot plasma from contacting the wallsof its reactor. In magnetic confinement, fusion occurs entirely withinthe plasma.

Most of the research in magnetic confinement is based on the tokamakdesign in which hot plasma is confined within a toroidal magnetic field.The Tokamak Fusion Test Reactor (TFTR) at Princeton, N.J. is world'sfirst magnetic fusion device to perform extensive scientific experimentswith plasmas composed of 50/50 deuterium/tritium. Built in 1980, it washoped that TFTR would finally achieve fusion energy, but it neverachieved this goal and was shut down in 1997. To date, the longestplasma duration time of any tokamak is 6 minutes and 30 seconds, held bythe Tore Supra tokamak in France. Current efforts in magneticallyconfined fusion are focused on the International ThermonuclearExperimental Reactor (ITER), a Tokamak reactor that began constructionin 2013. As of June 2015, the building costs have exceeded $14 billion,and construction of the facility is not expected until 2019 with fulldeuterium-tritium experiments starting in 2027. The current estimate forthe cost of the project is over $50 billion, and it is likely the costswill continue to rise. Recently, the Energy and Water DevelopmentSubcommittee of the Senate Appropriations Committee released arecommendation that the U.S. withdraw from the ITER project. Due tomarket realities, and the inherent limitations of the tokamak design forfusion power, many analysts doubt that fusion reactors such as ITER willbecome commercially viable.

An alternative form of magnetic confinement is being studied by theMaryland Centrifugal Experiment (MCX), at the University of Maryland. Itwill test the concepts of centrifugal confinement and velocity shearstabilization. In this experiment, capacitors are discharged from acylindrical cathode through hydrogen gas to a surrounding vacuum chamberin the presence of a magnetic field. The orthogonal electric andmagnetic fields (represented as J×B) produce a force that drives hotionized plasma (>10⁵ K) into rotation around the discharge electrodes.Due to the significant change in temperatures at the plasma boundary,there inevitably exists cold neutral species that significantly affectplasma flows. Studies have focused on the effect of neutrals and as theyhave thought to “impede the required plasma rotation” needed for fusionconditions. “Neutral species” or simply “neutrals” are atoms ormolecules with a neutral charge, i.e., they have the same number ofelectrons and protons, the atomic number in the case of an atom. An ionor ionized atom or other particle has a charge, i.e., it has at leastone more electron than proton or at least one more proton than electron.

Rotating plasma devices that do not employ highly ionized plasmas havebeen considered for fusion research, but the neutrals have always beenseen as a problem for reaching fusion conditions. Due to limitingeffects including neutral drag and instabilities, one researcher in thefield considered that while “not quite impossible [it is] still unlikelythat rotating plasmas alone would lead to the realization of aself-sustained fusion reactor.” (Review Paper: ROTATING PLASMAS”,Lehnert, Nuclear Fusion 11 (1971)).

All credible prior approaches have all faced confinement and engineeringissues. A gross energy balance for a fusion reactor, Q, is defined as:

Q=E _(fusion) /E _(in),

where E_(fusion) is the total energy released by fusion reactions, andE_(in) is the energy used to create the reactions. The goal is to exceeda Q of one or “unity” toward the end of creating a viable energy source.Officials of the Joint European Torus (JET) claim to have achieved Q≈0.7and the US National Ignition Facility recently claims to have achieved aQ>1 (ignoring the very substantial energy losses of its lasers). Thecondition of Q=1, referred to as “breakeven,” indicates that the amountof energy released by fusion reactions is equal to the amount of energyinput. In practice, a reactor used to produce electricity should exhibita Q value significantly greater than 1 to be commercially viable, sinceonly a portion of the fusion energy can be converted to a useful form.Conventional thinking holds that only strongly ionized plasmas that donot have significant quantities of neutrals present have the potentialof achieving Q>1. These conditions limit the particle densities andenergy confinement times that can be achieved in a fusion reactor. Thus,the field has looked to the Lawson criterion as the benchmark forcontrolled fusion reactions—a benchmark, it is believed, that no one hasyet achieved when accounting for all energy inputs. The art's pursuit ofthe Lawson criterion, or substantially similar paradigms, has led tofusion devices and systems that are large, complex, difficult to manage,expensive, and, as yet, economically unviable. A common formulation ofthe Lawson criterion, known as the triple product, is as follows:

${{nT}\; \tau_{E}} > {\frac{12k_{B}}{E_{ch}}\frac{T^{2}}{\langle{\sigma \; v}\rangle}}$

While the Lawson criterion will not be discussed in detail here; inessence, the criterion states that the product of the particle density(n), temperature (T), and confinement time (τ_(E)) must be greater thana number dependent on the energy of the charged fusion products(E_(ch)), the Boltzmann constant (k_(B)), the fusion cross section (σ),the relative velocity (υ), and temperature in order for ignitionconditions to be reached. For the deuterium-tritium reaction, theminimum of the triple product occurs at T=14 keV and the number for thetriple product is about 3×10²¹ keV s/m³ (J. Wesson, “Tokamaks”, OxfordEngineering Science Series No 48, Clarendon Press, Oxford, 2nd edition,1997.) In practice, this industry-standard paradigm suggests thattemperatures in excess of 150,000,000 degrees Centigrade are required toachieve positive energy balance using a D-T fusion reaction. Forproton-boron 11 fusion, the Lawson criterion suggests that the requiredtemperature must be yet substantially higher. More specifically, nτ˜10¹⁶s/cm³, which is ˜100× greater than required for D-T fusion [fromInertial Electrostatic Confinement (IEC) Fusion: Fundamentals andApplications by George H. Miley and S. Krupaker Murali].

An aspect of the Lawson criterion is based on the premise that thermalenergy must be continually added to the plasma to replace lost energy,maintain the plasma temperature, and keep it fully or highly ionized. Inparticular, a major source of energy loss in conventional fusion systemsis radiation due to electron bremsstrahlung and cyclotron motion asmobile electrons interact with ions in the hot plasma. The Lawsoncriterion was formulated for fusion methods where electron radiationloss is a significant consideration due to the use of hot, heavilyionized plasmas with highly mobile electrons.

Because the conventional thinking holds that high temperatures and astrongly-ionized plasma, absent of the presence of a significantpresence of neutrals, are required, it was further believed thatinexpensive physical containment of the reaction was impossible.Accordingly, the methods that have been most heavily pursued aredirected to complex and expensive schemes to contain the reaction, suchas those used in magnetic confinement systems (e.g., the ITER tokamak)and in inertial confinement systems (e.g., NIF laser).

In fact, at least one source acknowledges the believed impossibility ofcontaining a fusion reaction with a physical structure: “The simplestand most obvious method with which to provide confinement of a plasma isby a direct-contact with material walls, but is impossible for twofundamental reasons: the wall would cool the plasma and most wallmaterials would melt. We recall that the fusion plasma here requires atemperature of ˜10⁸ K while metals generally melt at a temperature below5000 K.” (“Principles of Fusion Energy,” A. A. Harms et al.). The needfor extremely high temperatures is premised on the belief that onlyhighly energized ions with charge can fuse, and that the coulombicrepulsion force limits the fusion events. The present teaching in thefield relies on this basic assumption for the vast majority of allresearch and projects.

In rare instances, researchers have considered methods for reducing theCoulombic barrier or repulsion force, which repels interacting positivenuclei, in order to reduce the required energy to initiate and maintainfusion. Such methods have largely been disregarded as infeasible withthe methods described above.

In the 1950's the concept of muon-catalyzed fusion was studied by LuisAlvarez using a hydrogen bubble chamber at the University of Californiaat Berkeley. Alvarez's work (“Catalysis of Nuclear Reactions by μMesons.” Physical Review. 105, Alvarez, L. W.; et al. (1957))demonstrated nuclear fusion taking place at temperatures significantlylower than the temperatures required for thermonuclear fusion. Intheory, it was proposed that fusion could occur even at or below roomtemperature. In this process, a negatively charged muon replaces one ofthe electrons in a hydrogen molecule. Since the mass of a muon is 207greater than an electron, the hydrogen nuclei are consequently drawn 207times closer together than in a normal molecule. When the nuclei arethis close together, the probability of nuclear fusion is greatlyincreased, to the point where a significant number of fusion events canhappen at room temperature.

While muon-catalyzed fusion received some attention, efforts to make amuon-catalyzed fusion source have not been successful. Currenttechniques for creating large numbers of muons require significantamounts of energy that exceed the energy produced by the catalyzednuclear fusion reactions, thus precluding breakeven or Q>1. Moreover,each muon has about a 1% chance of “sticking” to the alpha particleproduced by the nuclear fusion of a deuteron (the nucleus of deuteriumatom) with a triton (the nucleus of tritium atom), removing the “stuck”muon from the catalytic cycle. This means that each muon can onlycatalyze at most a few hundred deuterium-tritium nuclear fusionreactions. Thus, these two factors—muons being too expensive to make andthen sticking too easily to alpha particles—limit muon-catalyzed fusionto a laboratory curiosity. To create useful muon-catalyzed fusion,reactors would need a cheaper, more efficient muon source and/or a wayfor each muon to catalyze many more fusion reactions. To date, none havebeen found or even theorized.

In March of 1989, Martin Fleischmann and Stanley Pons submitted a paperto the Journal of Electroanalytical Chemistry reporting that they haddiscovered a method of reducing the Coulombic barrier by a method thatis now commonly referred to as “cold fusion.” Fleishmann and Ponsbelieved they had observed nuclear reaction byproducts and a significantamount of heat generated by a small tabletop experiment involvingelectrolysis of heavy water on the surface of palladium electrodes. Oneexplanation for cold fusion considered that hydrogen and its isotopescould be absorbed in certain solids, such as palladium, at highdensities. The absorption of hydrogen creates a high partial pressure,reducing the average separation of hydrogen isotopes and thus loweringthe potential barrier. Another explanation was that electron screeningof the positive hydrogen nuclei in the palladium lattice was sufficientfor lowering the barrier.

While the Fleischmann-Pons findings initially received significantpress, the reception by the scientific community was largely critical asa group at Georgia Tech University quickly found problems with theirneutron detector, and Texas A&M University discovered bad wiring intheir thermometers. These experimental mistakes, along with many failedattempts to replicate the Fleischmann-Pons experiment by well-knownlaboratories, lead most in the scientific community to conclude that anypositive experimental results should not be attributed to “fusion.” Duein part to the publicity received, the United States Department ofEnergy (DOE) organized a special panel to review cold fusion theory andresearch. First in November of 1989, and again 2004, the DOE concludedthat results thus far did not present convincing evidence that usefulsources of energy would result from the phenomena attributed to “coldfusion.”

Another attempt to reduce the Coulombic barrier employs electronscreening in a solid matrix. Electron screening has first been observedin stellar plasmas where it was determined to change the fusion rate byfive orders of magnitude if the screening factor changes by only a fewpercent (Wilets, L., et al. “Effect of screening on thermonuclear fusionin stellar and laboratory plasmas.” The Astrophysical Journal 530.1(2000): 504.). According to Wilets, “[t]he rate of thermonuclear fusionin plasmas is governed by barrier penetration. The barrier itself isdominated by the Coulomb repulsion of the fusing nuclei. Because thebarrier potential appears in the exponent of the Gamow formula, theresult is very sensitive to the effects of screening by electrons andpositive ions in the plasma. Screening lowers the barrier and thusenhances the fusion rate; the greater the nuclear charges, the moreimportant it becomes.”

One example that tries to make use of this electron screening effect tocreate ignition conditions is presented in US Patent Publication No.US2005/0129160A1 by Robert Indech. In this application, Indech describesthe electron shielding of the positively-charged repulsive forcesbetween two deuterons located near the tip of a microscopic conestructure when electrons concentrate at the top of the cone structuredue to an applied potential. As disclosed, these cones were arrayed on asurface measuring 3 cm by 3 cm.

While Indech and others have realized the potential electron screeningto lower the Coulombic barrier for fusion reactors, it is doubtful anyefforts have been successful. At most these efforts appear to proposemethods for ignition and not a sustained and controlled fusion reaction.Despite efforts in ICF, magnetic confinement fusion, and various methodsof reducing the Coulombic barrier, there is currently no commerciallyfeasible fusion reactor design that exists.

SUMMARY

An aspect of this disclosure pertains to “hybrid” reactors that includetwo modes of driving neutrals and charged species into rotation: onerelying solely on electric field, specifically an electric field thatvaries azimuthally around the rotation path, and one relying electricand magnetic fields (typically manifest as a Lorentzian force).Therefore, the hybrid reactors may have a plurality of azimuthallydistributed electrodes for generating electric field only rotation, atleast one magnet for producing a Lorentzian force on charged particles.In some embodiments, the azimuthally distributed electrodes serve rolesin both types of rotation; that is, they can produce an electric fieldthat interacts with the magnetic field to produce a Lorentzian force onthe charged particles. In other embodiments, a separate set ofelectrodes (not among the azimuthally distributed electrodes) producesthe electric field that interacts with the magnetic field. In someembodiments, the two modes of generating rotation are appliedsequentially, with or without temporal overlap. For example, theLorentzian mode may be applied first, and only later, after particlesare undergoing rotational movement, is the azimuthally varying electricfield applied.

The Lorentzian rotor mode can be implemented in at least two differentbasic geometries: (1) a substantially axial magnetic field and asubstantially radial electric field, and (2) a substantially axialelectric field and a substantially radial magnetic field.

In certain embodiments employing a substantially axially directedmagnetic field, hybrid reactors (apparatus) may be characterized by thefollowing elements: (a) a confining wall having a substantiallycylindrical inner surface that has an axis, where the confining wall atleast partially encloses a confinement region; (b) a plurality ofelectrodes azimuthally distributed along the confining wall; (c) aninlet to the confinement region for permitting introduction of neutralsto the confinement region; (d) at least one magnet configured to providea magnetic field in the confinement region such that the magnetic fieldis directed at least in part in the direction of the axis of thesubstantially cylindrical inner surface; (e) a control system having avoltage and/or current source; and (f) a reactant attached to orembedded in the confining wall such that, during operation, repeatedcollisions between the neutrals and the reactant produce an interactionwith the reactant that gives off energy and produces a product having anuclear mass that is different from a nuclear mass of any of the nucleiof the neutrals and the reactant. The control system may be configured(e.g., programmed) to (i) sequentially apply one or more potentials toeach of the plurality of electrodes to induce and/or maintain rotationalmovement of ions and the neutrals in the confinement region, (ii)produce an electric field in the confinement region directed at least inpart in a radial direction with respect to the substantially cylindricalinner surface, where the electric field interacts with the magneticfield to induce and/or maintain the rotational movement of ions and theneutrals in the confinement region, and (iii) transition between (i) and(ii).

In certain embodiments, a first electrode forming at least a portion ofthe confining wall and a second electrode located within a regioninterior to the first electrode and separated from the first electrodeby at least the confinement region, and the control system is configuredto produce the electric field in the confinement region by applying apotential difference between the first electrode and the secondelectrode. This is an example of an apparatus that can produce asubstantially radially directed electric field.

In some embodiments, the apparatus has an inner wall within a regioninterior to the inner surface of the confining wall and separated fromthe confining wall by at least the confinement region; and a secondplurality of electrodes azimuthally distributed along the inner wall. Insuch embodiments, the control system may be further configured tosequentially apply one or more potentials to each of the secondplurality of electrodes. This is another example of an apparatus thatcan produce a substantially radially directed electric field. In someimplementations, the inner wall is separated from the inner surface ofthe confining wall by a distance of, on average, about 1 mm to 50 cm.

In certain embodiments that employ a substantially radially directedmagnetic field, hybrid reactors (apparatus) may be characterized by thefollowing elements: (a) a confining wall having a substantiallycylindrical inner surface that has an axis, where the confining wall atleast partially encloses a confinement region; (b) a plurality ofelectrodes azimuthally distributed along the confining wall; (c) aninlet to the confinement region for permitting introduction of neutralsto the confinement region; (d) at least one magnet configured to providea magnetic field in the confinement region such that the magnetic fieldis directed at least in part in a radial direction with respect to thesubstantially cylindrical inner surface; (e) a control system having avoltage and/or current source; and (f) a reactant attached to orembedded in the confining wall such that, during operation, repeatedcollisions between the neutrals and the reactant produce an interactionwith the reactant that gives off energy and produces a product having anuclear mass that is different from a nuclear mass of any of the nucleiof the neutrals and the reactant. The control system may be configured(e.g., programmed) to (i) sequentially apply one or more potentials toeach of the plurality of electrodes to induce and/or maintain rotationalmovement of ions and the neutrals in the confinement region, (ii) applya potential difference between two of the plurality of electrodes toproduce an electric field in the confinement region such that theelectric field is directed at least in part in an axial direction withrespect to the substantially cylindrical inner surface, where theelectric field interacts with the magnetic field to induce and/ormaintain the rotational movement of ions and the neutrals in theconfinement region, and (iii) transition between (i) and (ii).

In embodiments employing a substantially radially directed magneticfield, the at least one magnet may include (i) a first ring magnetdefining or disposed on at least part of the confining wall; and (ii) asecond ring magnet located within a region interior to and substantiallyconcentric with the first ring magnet, where the second ring magnet isseparated from the from the first ring magnet by at least theconfinement region.

In embodiments employing a substantially radially directed magneticfield, the plurality of electrodes may include a first set of electrodesazimuthally distributed along the confining wall on a first axial sideof the confining wall and a second set of electrodes azimuthallydistributed along the confining wall on a second axial side of theconfining wall, opposite the first axial side of the confining wall,where the control system is configured to apply the potential differencebetween at least one electrode of the first set of electrodes and atleast one electrode of the second set of electrodes. The control systemmay then, in some cases, be configured to: apply the potentialdifference between all or a substantial fraction of the electrodes inthe first set of electrodes and all or a substantial fraction of theelectrodes in the second set of electrodes at the same time to producethe electric field in the confinement region that is directed at leastin part in an axial direction with respect to the substantiallycylindrical inner surface; and afterwards sequentially apply the one ormore potentials to each of the plurality of electrodes in an azimuthallysequential manner to maintain the rotational movement of the ions andneutrals in the confinement region.

In some embodiments, regardless of the directionality of the appliedelectrical and magnetic fields, the apparatus may have one or more ofthe following features: the apparatus includes at least four electrodes;the confining wall is a layered structure in which at least one thelayers includes the plurality of azimuthally distributed electrodes; theinteraction that occurs during operation of the apparatus is a fusionreaction (e.g., an aneutronic fusion reaction); the reactant attached toor embedded in the confining wall includes boron-11; and the neutralsinclude neutral hydrogen.

To facilitate the interaction between neutrals and the reactant, theapparatus may be configured so that, during operation, the confinementregion proximate the confining wall includes an electron rich regionhaving an excess of electrons over positively charged particles of atleast about 10⁶/cm³. In certain embodiments, the electron rich regionhas an electric field strength of at least about 10⁶ V/m. In certainembodiments, the electron rich region has an energy of, on average, ofbetween about 0.1 eV and 2 eV.

In some embodiments, regardless of the directionality of the appliedelectrical and magnetic fields, the control system may be configured forone or more of the following operations: sequential application ofelectric potentials to each of the plurality of electrodes according toa timing sequence that defines a speed of the rotational movement of theions and the neutrals in the confinement region; control of the magneticfield in the confinement region; and control of a supply of neutrals tothe confinement region via the inlet.

In certain embodiments, the apparatus includes one or more electronemitters configured to, during operation, emit electrons into a regionadjacent to the confining wall. In some implementations, the electronemitters include boron or a boron-containing material.

Another aspect of the disclosure pertains to a method of operating areactor (apparatus) that is characterized by: a confining wall having asubstantially cylindrical inner surface that has an axis, where theconfining wall at least partially encloses a confinement region; aplurality of electrodes azimuthally distributed along the confiningwall; an inlet to the confinement region for permitting introduction ofneutrals to the confinement region; at least one magnet configured toprovide a magnetic field in the confinement region such that themagnetic field is directed at least in part in the direction of the axisof the substantially cylindrical inner surface; and a reactant attachedto or embedded in the confining wall. The method may be characterized bythe following operations: (i) sequentially applying one or morepotentials to each of a plurality of electrodes azimuthally distributedalong a confining wall to induce and/or maintain rotational movement ofions and the neutrals in a confinement region; (ii) producing anelectric field in the confinement region directed at least in part in aradial direction with respect to the substantially cylindrical innersurface, where the electric field interacts with the magnetic field toinduce and/or maintain the rotational movement of ions and neutrals inthe confinement region; and (iii) transitioning between (i) and (ii).When the method is performed, repeated collisions between the neutralsand the reactant produce an interaction with the reactant that gives offenergy and produces a product having a nuclear mass that is differentfrom a nuclear mass of any of the nuclei of the neutrals and thereactant.

In some cases, producing the electric field in the confinement regionmay include applying a potential difference between a first electrodeand a second electrode, where the first electrode forms at least aportion of the confining wall and the second electrode is located withina region interior to the first electrode and separated from the firstelectrode by at least the confinement region.

Methods of operating a reactor may additionally include sequentiallyapplying one or more potentials to each of a second plurality ofelectrodes, where the second plurality of electrodes is azimuthallydistributed along an inner wall the reactor, where the inner wall iswithin a region interior to the inner surface of the confining wall andseparated from the confining wall by at least the confinement region.The inner wall, in some cases, may be separated from the inner surfaceof the confining wall by a distance of, on average, about 1 mm to about50 cm.

Another aspect of the disclosure pertains to a method of operating areactor (apparatus) that is characterized by: a confining wall having asubstantially cylindrical inner surface that has an axis, wherein theconfining wall at least partially encloses a confinement region; aplurality of electrodes azimuthally distributed along the confiningwall; an inlet to the confinement region for permitting introduction ofneutrals to the confinement region; at least one magnet configured toprovide a magnetic field in the confinement region such that themagnetic field is directed at least in part in a radial direction withrespect the substantially cylindrical inner surface; and a reactantattached to or embedded in the confining wall. The method ischaracterized by the following operations: (i) sequentially applying oneor more potentials to each of the plurality of electrodes azimuthallydistributed along a confining wall to induce and/or maintain rotationalmovement of ions and the neutrals in a confinement region; (ii) applyinga potential difference between two of the plurality of electrodes toproduce an electric field in the confinement region such that theelectric field is directed at least in part in an axial direction withrespect to the substantially cylindrical inner surface, where theelectric field interacts with the magnetic field to induce and/ormaintain the rotational movement of ions and the neutrals in theconfinement region; and (iii) transitioning between (i) and (ii). Asdescribed in other aspects, repeated collisions between the neutrals andthe reactant produce an interaction with the reactant that gives offenergy and produces a product having a nuclear mass that is differentfrom a nuclear mass of any of the nuclei of the neutrals and thereactant.

In some cases, the at least one magnet may include a first ring magnetdefining or disposed on at least part of the confining wall; and asecond ring magnet located within a region interior to and substantiallyconcentric with the first ring magnet, where the second ring magnet isseparated from the from the first ring magnet by at least theconfinement region.

In some cases, the plurality of electrodes may include a first set ofelectrodes azimuthally distributed along the confining wall on a firstaxial side of the confining wall and a second set of electrodesazimuthally distributed along the confining wall on a second axial sideof the confining wall, opposite the first axial side of the confiningwall. A potential difference can then be applied between at least oneelectrode of the first set of electrodes and at least one electrode ofthe second set of electrodes. In some cases, applying the potentialdifference between two of the plurality of electrodes includes applyingthe potential difference between all or a substantial fraction of theelectrodes in the first set of electrodes and all or a substantialfraction of the electrodes in the electrodes in the second set ofelectrodes at the same time to produce the electric field in theconfinement region that is directed at least in part in an axialdirection with respect to the substantially cylindrical inner surface,and thereafter sequentially applying the one or more potentials to eachof the plurality of electrodes in an azimuthally sequential manner tomaintain the rotational movement of the ions and neutrals in theconfinement region.

In some cases, e.g., for a reactor having a radially or axially directedmagnetic field, sequentially applying one or more potentials to each ofthe plurality of electrodes includes applying the one or more potentialsaccording to a timing sequence that defines a speed of the rotationalmovement of the ions and the neutrals in the confinement region. In somecases, a reactor has at least four electrodes, and in some cases, theconfining wall has a layered structure in which at least one the layersincludes the plurality of azimuthally distributed electrodes along theconfining wall. In certain embodiments, the interaction is a fusionreaction such as an aneutronic fusion reaction. In some cases, thereactant embedded in the confining wall includes boron-11 and theneutrals include neutral hydrogen.

In some cases, methods can include an operation that causes one or moreelectron emitters to emit electrons into a region adjacent to theconfining wall. Electron emitters can include, e.g., boron orboron-containing material.

In certain embodiments, the above methods additionally include producingan electron rich region having an excess of electrons over positivelycharged particles of at least about 10⁶/cm³, where the electron richregion is proximate the confining wall the confinement region. Theelectron rich region may have an electric field strength of at leastabout 10⁶ V/m. The neutrals in the electron rich region may have anenergy of, on average, of between about 0.1 eV and 2 eV.

Methods of operating reactors which employ a substantially radially or asubstantially axially directed magnetic field may further includecontrolling the magnetic field in the confinement region and/orcontrolling a supply of neutrals to the confinement region via theinlet. In certain embodiments, the rotational movement of the neutralsin the confinement region is provided at an average velocity of at leastabout 50,000 m/s.

These and other features of the disclosure will be described below inmore detail and with reference to the associated drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIGS. 1a-c depict several views of a first embodiment reactor.

FIGS. 2a-b schematically illustrate the movement of charged particlesand neutral particles rotating within a confinement wall.

FIGS. 3a-d schematically depict neutral and charged particleinteractions with a confinement wall.

FIGS. 4a-e depict stages of the aneutronic proton-boron-11 fusionreaction.

FIGS. 5a-d depict a reverse electrical polarity reactor.

FIGS. 6a-f depict a hybrid reactor.

FIGS. 7a-b depict a wave-particle reactor.

FIGS. 8a-b depict various electrode configurations of a first embodimentreactor.

FIGS. 9a-c depict various cross sections of a first embodiment reactor.

FIGS. 10a-d depict a first embodiment reactor in which an axial magneticfield is applied by a superconducting magnet.

FIGS. 11a-b depict a first embodiment reactor in which permanent magnetsare configured to apply an axial magnetic field in a first embodimentreactor.

FIGS. 12a-b depict a first embodiment reactor in which the appliedmagnetic field in the confinement region is applied using permanentmagnets.

FIGS. 13a-c depict a configuration of a first embodiment reactor.

FIGS. 14a-c depict a configuration of a first embodiment reactor.

FIGS. 15a-c depict how ring magnets may be positioned along a commonaxis create a magnetic field substantially pointed along that axis.

FIGS. 16a-c depict a first embodiment reactor in which the appliedmagnetic field in the confinement region is applied using ring magnets.

FIGS. 17a-c depict a first embodiment reactor in which the appliedmagnetic field in the confinement region is applied using radiallyoffset magnets.

FIGS. 18a-d depict a first embodiment reactor in which the appliedmagnetic field in the confinement region is applied using anelectromagnet.

FIGS. 19a-b depict various embodiments of a reverse electrical polarityreactor.

FIGS. 20a-b depict various electron emitters that may be placed on aconfinement wall.

FIGS. 21a-b depict electron emitting modules that may be placed on aconfinement wall of a reactor.

FIG. 22 depicts a reactor configured with a laser increasing orcontrolling electron emission from an electron emitter.

FIGS. 23a-c depicts a configuration where nuclear magnetic resonancesensing is used to determine the composition of gas reactants within areactor.

FIG. 24 depicts how a control system may be configured to operate areactor using closed-loop feedback.

FIG. 25 depicts an example of a multistage process flow that may be usedto operate a reactor

DETAILED DESCRIPTION Introduction

Various embodiments disclosed herein pertain to reactors and methods ofoperating those reactors under conditions that induce a reaction betweentwo or more nuclei in a manner that produces more energy than is inputto the reactor. This disclosure refers to such reactions as nuclearfusion reactions or simply fusion reactions, although aspects of thereaction may be quantitatively or qualitatively different from aspectsof reactions conventionally characterized as nuclear fusion. Thereforewhen the term fusion is used in the remainder of this disclosure, theterm does not necessarily connote all the features conventionallyascribed to nuclear fusion. In some embodiments disclosed herein, areactor may generate a sustained fusion reaction making it suitable as aviable energy source. As described herein, a sustained fusion reactionrefers to a fusion reaction in which reactor may continuously operateabove unity for a period of about a second.

In various embodiments, the reactor in which the fusion reaction occursis designed or configured to constrain or confine rotating speciesincluding, typically, one or more of the nuclei participating in afusion reaction. Various structures may be provided for confining therotating species. Typically, though not necessarily, these structuresdefine a solid physical enclosure. As explained more fully elsewhereherein, the enclosed structure may have many shapes such as a generallycylindrical shape. Examples of suitable structures that may be used fora physical enclosure are depicted in FIGS. 1, 7, and 6.

Regardless of any other functions, the wall of the reactor typicallyserves to confine species rotating in the region adjacent to andinternal to the wall. The wall is confining in the sense that itconfines the rotating species to remain within the reactor. As describedherein, this wall of the reactor is referred to as the wall, theconfining wall, or the shroud. In various embodiments, the wall alsoserves other functions: notably as an electrode, as a magnet, as asource of fusion reactants (e.g., boron compounds), and/or as anelectron emitter. Because the wall constrains the reactants speciesphysically rather than by a magnetic field or a pressure wave—as aredone in conventional approaches to fusion—it is unlike any conventionalfusion reactor designs. Its other functions, such as being an electrodefor imparting a voltage difference, being a magnet, being a source ofreactant material, and being an electron emitter, provide additionaldistinctions from conventional fusion reactor designs.

In certain embodiments, the reactor contains a wall, as described, and aspace interior to the wall (which may be annular in shape) wherereactant species, including a substantial fraction or percentage ofneutrals, rotate and repeatedly impinge on the surface of the reactorwall and sometimes fuse with species present in the wall. Whenaccounting for the energy input to the reactor, the resulting reactioncan breakeven and result in Q>1. To ensure that the fusion reaction issustainable over a period required by particular energy-generationapplications, the ratio of energy out to energy in should besignificantly greater than 1. This accounts for inherent inefficienciesin using energy generated by a fusion reaction to sustain the conditionsthat allow fusion to occur (e.g., particular plasma densities in theconfinement region). In certain embodiments, the ratio should be atleast about 1.2. In certain embodiments, the ratio should be at leastabout 1.5. In certain embodiments, the ratio should be at least about 2.In certain embodiments, the reactor is continuously operated undersustainable conditions for at least about fifteen minutes, or at leastabout one hour. In one example, hydrogen atoms rotate in the reactor andimpinge on boron or lithium atoms in the reactor wall to undergo fusion.In some embodiments, the reactor includes one or more electron emittersthat produce an electron flux that, during operation, produce a strongfield that reduces the Coulombic repulsion between interacting nuclei.

The reactants can be any species that can support a fusion reaction inthe space interior to the confining wall of the reactor. In variousembodiments, at least one of the reactants is a species that is rotatingwithin the reactor interior region. In some cases, both of the reactantsare rotating species. In some cases, one of the reactants is a rotatingspecies and the other is a species that is held stationary, such as whena reactant is embedded in a part of the reactor wall that confines therotating species. In some cases, there is some combination of reactantsthat are rotating and stationary such that fusion may occur betweenrotating species or between a rotating species and a stationary species.In cases where the reacting species are predominantly rotating species,the physical structure of the reactor may be configured such that therotating species need not substantially impinge on the inner surface ofa wall of the reactor to support a fusion reaction. In some designs, therotating species are constrained by a force such as a force thatprevents them from substantially striking the reactor wall. In suchdesigns, two rotating species fuse in the region interior to theconfining wall (e.g., the confinement region) or along the surface ofthe wall. In some designs, a rotating species may fuse with a stationaryspecies (e.g., a target material) located within the confinement region.

In certain embodiments, the reactants are species that reactaneutronically. In other embodiments, the reactants are species thatreact neutronically. One or both of the reactants may also be a neutral,or uncharged, species. Sometimes the species present in the reactor arereferred to as “particles.” However, such species are only particles atthe molecular or atomic scale.

The disclosed small-scale, e.g., table-top, aneutonic reactors requirerelatively little or no biological shielding from neutron radiation.Fusion reactions in reactors described herein may be characterized as“warm fusion,” e.g., where fusion occurs in the temperature range ofabout 1000K to 3000K, and as such are much easier to handle compared to“hot fusion reactors” (e.g. those in tokamak reactors). Since the fusionis substantially aneutronic and “warm,” materials and thus costsassociated with “warm fusion” reactors may be significantly reduced. Forinstance, in some cases, a prototype reactor has been built for lessthan $50,000. Since radiation shielding and the industrial-gradehardware commonly used for hot plasma reactors may not be required, thedisclosed small-scale reactors may also have a small weight andfootprint.

The rotational motion of the species in the reactor may be imparted by anumber of mechanisms. One mechanism imparts rotation via the applicationof interacting electric and magnetic fields. The interaction is manifestas a Lorentzian force that acts on charged particles in the reactor.Examples of reactor designs that can produce a Lorentzian force to acton charged species are depicted in FIGS. 1a-c and 6. FIGS. 1a-c depict aLorentzian driven reactor where the reactor has inner electrode 120, andwhere the shroud (confining wall) is an outer electrode 110. An electricfield 144 between the electrodes in the presence of an applied magneticfield 146, having a perpendicular component, causes a Lorentzian forceon charge particles or charged species traveling in between theelectrodes. This force drives them azimuthally into rotation asindicated in FIG. 1c . In another class of reactor design, rotationalmotion is imparted to charged species by applying a potential or achange in potential sequentially to a plurality of electrodes arrangedazimuthally around a wall of the reactor. An example of a suitablereactor design is shown in FIG. 7.

In many implementations, the reactor is operated in a manner such thatthe rotating charged species interact with neutral species and impartangular momentum to those neutral species, thereby setting up rotationalmotion of the neutral species as well as the charged species within thereactor. In many implementations, the majority of rotating species areneutrals and the charged species are ionized particles such as a proton(p⁺). As described herein, this process may be referred to asion-neutral coupling. FIG. 2a schematically illustrates the ion-neutralcoupling process in which a few charged particles 204 impart motion tothe surrounding neutral particles 206.

In various embodiments, the reactor is designed to emit electrons in aninternally localized region of the reactor where fusion events areexpected to occur. Referring again to FIG. 2a , these electrons may forman electron-rich region 232 near the confining wall 210. The presence ofexcess electrons lowers the Coulomb barrier and thereby increases theprobability of fusion. As explained elsewhere herein, emitting electronsin this manner can produce an electron-rich region that reduces theintrinsic Coulombic repulsion between two positively charged nuclei,which are candidates for fusion. In certain embodiments, the electronemission occurs at or adjacent to the wall that confines the rotatingspecies within the reactor. In one example, electron emission isprovided by passive structures such as boron-containing coupons orstrips embedded in or attached to the confining wall of the reactor.Such passive structures emit electrons when the localized temperaturesincrease during operation of the reactor. In other embodiments, electronemission is implemented using active structures that are controlledindependently of the heating produced during normal operation of thereactor. An example of an active structure for electron emission isdepicted in FIGS. 21a and 21b and includes separately controlledresistive elements for heating the individual electron emitters.

Another aspect of this disclosure relates to structures or systems forcapturing and converting energy produced by a fusion reaction within thereactor. One class of energy capture systems provides for direct captureof electrical energy produced by traveling alpha particles generated bythe fusion reaction. This may be done by generating an applied electricfield in the path of emitted alpha particles which causes the alphaparticles to decelerate and generates an electric current in a circuitconnected to the electrodes used to produce the electric field. Anotherclass of energy capture systems provides for energy capture using heatengines such as those including a turbine, heat exchanger, or otherconventional structure employed to convert thermal energy produced fromthe fusion reaction into mechanical energy. These and other energycapturing mechanisms will be discussed later in this disclosure.

Interactions by Neutrals with the Wall

Neutral species interacting with the wall of a reactor provide adifferent type of interaction than has been employed in conventionalfusion studies. The repeated interactions take place over a relativelylarge volume, which may be the annular space next to the inner wall ofor the inner surface of the confinement wall. Because the rotatingneutrals frequently interact elastically with the wall at a shallowangle, e.g., at a glancing or grazing angle, they may immediately leavethe wall and reenter the interior space with much of the energy they hadupon entry. FIG. 2b illustrates an example trajectory path a neutral 206may have as it moves along the surface of the confinement wall 210. Whena rotating neutral particle enters or strikes the wall, it typicallyencounters a potential fusion partner with which it may react or not.When it does not react, it re-enters the interior space where itcontinues on its rotational journey. In this manner, it repeatedlyinteracts with the surface of the wall, and in each such elasticcollision little to no energy is lost.

Some particle-wall interactions that do not result in fusion areillustrated schematically in FIGS. 3a-d . While the figures depictinteractions with boron¹¹ and/or titanium, these interactions may alsooccur when other reactant materials are used in the confinement wall. Asillustrated in FIG. 3a , in some fraction of the neutral-wallinteractions, the neutral particle experiences an elastic collision witha nucleus in the wall (in this case an atom of boron¹¹), and therebounding neutral maintains most of the energy it had going into theinteraction. Of all neutral-wall interactions, elastic collisionstypically have that highest occurrence. In a much smaller fraction ofthe collisions, depicted in FIG. 3b , the nucleus of the neutral comessufficiently close to the nucleus of an atom in the wall that thecollision becomes inelastic as a result of tunneling that occurs whenthe two nuclei come into very close proximity. FIG. 3c depicts yetanother interaction that may occur; in this case, a neutral penetratesinto the wall. This type of collision may occur somewhat frequently whenthe confinement surface contains a material such as titanium orpalladium that may absorb hydrogen molecules.

FIG. 3d depicts an inelastic collision of a charged particle, e.g., aproton, with the confining wall. This situation contrasts with thefrequent elastic collisions that neutrals such as atomic hydrogen havewith the confining wall (previously depicted in FIG. 3a ). When acharged particle approaches and departs from the confining wall, theparticle may experience Bremsstrahlung energy loss. This energy loss iscaused by electrostatic interaction between the charged particle andelectrons in the electron-rich region. As a result of the electrostaticforces, some kinetic energy is lost, and high energy electromagneticradiation such as x-rays are emitted. In conventional fusion reactorsthat focus on trying to fuse ionized particles, Bremsstrahlung radiationmay result in significant energy loss. By using a weakly ionized plasmahaving a high proportion of neutrals to ions, these losses are largelyavoided.

In a certain fraction of tunneling interactions between the neutralnucleus in motion and the nucleus of an atom in the wall, fusion mayoccur. FIG. 4a depicts the stages of the aneutronic fusion reaction thatoccurs when a hydrogen atom or proton fuses with a boron 11 atom. First,in 482, a proton traveling at high velocity collides with a boron 11atom, and the two nuclei fuse to form an excited carbon nucleus,depicted in 483. The excited carbon nucleus is short-lived, however, anddecomposes into a beryllium nucleus and an alpha particle that isemitted having a kinetic energy of 3.76 MeV, as seen in 484. Finally, in485, the newly formed beryllium nucleus almost immediately decomposesinto two more alpha particles, each having a kinetic energy of 2.46 MeV.FIGS. 4b-e depict the various stages of the same proton-boron 11 fusionreaction shown in FIG. 4a in relation to the surface of the confiningwall 412. FIG. 4a depicts a proton traveling at high velocity towards asurface of boron 11 atoms on the confining wall. As the neutral hydrogenatom approaches the confining wall it passes through and theelectron-rich region 432, which partially screens the repulsive forcebetween the two positively charged nuclei. FIG. 4c depicts the stage atwhich the neutral hydrogen has fused with a boron atom to form a carbonnucleus. In FIG. 4d , the carbon nucleus has decomposed into a berylliumnucleus one alpha particle. Lastly, in FIG. 4e , the beryllium nucleusdecomposes, emitting two additional alpha particles. Because thepotential reactants are neutral species rather than ions, most of theirinteractions with atoms in the surface of the confinement wall areelastic collisions. In contrast, a positively charged particle enteringthe wall will be deflected by electrostatic repulsive forces at adistance from other nuclei in the wall. These electrostatic interactionscause the charged particle to lose energy; i.e., the collisions areinelastic. A neutral particle, which has a positively charged nucleusscreened to a degree by the orbital electrons, does not experience thesame repulsive force. As a consequence, the neutral is more likely todirectly impact another atom in the wall. The use of neutrals ratherthan ions, therefore, increases the likelihood of a fusion reaction, andwhen a fusion reaction does not occur, the neutral is more likely torebound elastically with a higher energy than a corresponding ion.

Overall, the rotating neutral particles undergo many repeatedinteractions with the wall and those that are unproductive in producinga fusion reaction elastically rebound with relatively little energyloss. As mentioned, the neutrals tend to reemerge from the wall and withsufficient energy that they can enter into a next interaction with thewall which might be productive in creating a fusion reaction. Each ofthe interactions with the wall has a probability of resulting in afusion reaction between the neutral nucleus and the nucleus of an atomin the wall.

Where the reactants are different species (e.g., ¹¹B and p⁺), the rateof fusion per unit volume is given by

dN/dT=n ₁ n ₂ σ v

where n₁ and n₂ are the densities of the respective reactants, σ is thefusion cross section at a particular energy, and v is the relativevelocity between the two interacting species. For a system in which atleast one species rotates in a confinement region and repeatedly strikesa confining wall containing a second species, the values of thedensities of the species may be on the order of 10²⁰ cm⁻³ for therotating species and 10²³ cm⁻³ for the immobilized species (e.g.,boron), the values of the fusion cross section may be on the order of10⁻³² cm², and the relative velocity of the interacting species may beon the order of 10³ m/s. By comparison, for a tokamak reactor, thevalues of the density of each of the species is on the order of 10¹⁴cm⁻³, the values of the fusion cross section are on the order of 10⁻²⁸cm², and the relative velocity of the interacting species is on theorder of 10⁶ m/s. (Based on information provided in “InertialConfinement Fusion.pdf” by M. Ragheb dated on Jan. 14, 2015.) Clearly,systems employing neutral species, like those described herein, have astrong advantage by virtue of their higher densities. The rate of fusionenergy per unit volume for such systems exceeds that of tokamak andinertial confinement systems by at least about eight orders ofmagnitude. Thus, a system as disclosed herein can achieve a defined rateof energy production in about one-hundred-millionth of the volume of atokamak or internal confinement system.

Coulombic Barrier Reduction

As explained, credible, prior approaches to nuclear fusion haveenergized fusion reactants and the supporting environment to extremelyhigh temperatures, on the order of at least 150,000,000K (13000 eV).This is done to impart sufficient kinetic energy to the fusion reactantsto overcome their natural electrostatic repulsion. In this environment,each reactant is a nucleus having an intrinsic positive charge whichmust first be overcome to allow some probability of a fusion reaction.

Certain embodiments of the present disclosure employ much lowertemperatures; e.g., on the order of 2000K (0.17 eV) in fusion reactions.These embodiments employ neutral species as one or more reactants and/ormodify the reaction environment to reduce the strong Coulombic repulsiveforce between reactant nuclei. Reduction of the Coulombic force may beaccomplished in various ways including, for example, (i) providing anelectron rich field in the region of the reaction and/or (ii) aligningthe quantum mechanical spins of reactant nuclei. Depending on thestructure of the reactor, the apparatus and methods for reducingCoulombic repulsion may take many forms. The following descriptionassumes that the reactor includes an annular space with an outerconfining wall or shroud. Other reactor structures can likewise producereduced Coulombic repulsion environments that support fusion, but theymay accomplish this in manners different than the one that follows.

The following is provided as one possible explanation of the environmentnear the inner surface of a confining electrode and should not beconstrued as a limitation on the practice of the disclosed embodiments.In this explanation, reactant species, particularly neutrals, rotate athigh velocity and strike the inner surface of the electrode.Concurrently, electrons are emitted from or near the confining wall. Therapidly rotating neutrals have high angular velocity and therefore exertextreme pressure on the inner surface of the confining wall through anassociated centrifugal force. Electrons emitted from the inner surfaceof the wall oppose this force.

The emitted electrons will diffuse away from the location where they areemitted, e.g., away from the wall and toward an interior space. However,the centrifugal force of the neutrals constrains the electrons to theregion near the inner surface of the outer electrode. A resulting thinregion of balanced forces adjacent to the inner surface of the electrodepossesses a strong field that reduces the Coulombic repulsion betweenreactant nuclei.

The force balance may be expressed mathematically as the equilibrium of(i) the gradient (in a direction away from the wall surface in whichelectrons are emitted) of the product of the temperature and the densityof electrons and neutrals, and (ii) the centrifugal force exerted towardthe inner surface. The centrifugal force is proportional to the productof the neutrals' density, the radial position, and the square of theirangular velocity.

${\frac{\partial}{\partial }\left( {{n_{e}{KT}_{e}} + {n_{0}{KT}_{0}}} \right)} = {n_{0}m_{0}\omega^{2}}$

In this expression, r is the radial direction away from the innersurface of the confining electrode, K is the Boltzmann constant, T_(e)and T₀ are the electron and neutral temperatures in Kelvin, n_(e) and n₀are the densities of electrons and neutrals, n₀ is the density ofneutral species, m₀ is the mass of one rotating neutral species (e.g., ahydrogen atom), and ω² is the square of the angular velocity of therotating neutral species.

In a thin region next to the surface from which the electrons areemitted (e.g., the inner surface of the confining wall), the freeelectrons create a strong electrical field (see the schematicrepresentation of electron-rich region 232 adjacent confining wall 210in FIGS. 2a-b ). The high concentration of neutrals limits the mean freepath of the electrons, preventing them from following ballistictrajectories and thus obtaining sufficient kinetic energy tosignificantly ionize the neutrals. Also, there are relatively fewpositive ions available for recombination because the neutrals have asignificantly higher density than the ions. For example, the prevalenceof ions to neutrals may be in the ranges of less than about 1:10, lessthan about 1:100, less than about 1:1000, or less than about 1:10000.Hence the neutrals are frequently positioned between the electrons andpositive ions. This set of conditions produces a high concentration ofexcess electrons near the confining wall's inner surface and hence astrong electric field.

The combination of a large excess of electrons (over ions) in a verythin region (e.g., next to the inner surface of the electrode) and inthe presence of a high concentration of neutrals produces a very strongelectric field. In this region, the strong field reduces the Coulombicrepulsion of interacting positively charged nuclei. Hence, theprobability of two positively charged nuclei coming in close proximityis significantly increased.

Additionally, as mentioned, rotating particles impinging on the innersurface of the confining wall produce repeated opportunities forinteracting fusion reactants. Neutrals repeatedly pass through theelectron-rich layer and strike the inner surface of the confining wallor shroud and reenter the interior space of the reactor. Thisimpingement on the wall represents the radial component of centrifugalforce produced by particles rotating in a constrained environment (e.g.,the inner surface of the confining wall). The repeated collisions,contact, or strikes increase the probability of a fusion reaction in agiven area over a given period of time. The repetition replaces the needfor a long confinement time and addresses the concerns that led toLawson's criterion for characterizing prior approaches to fusionreactions. In simple terms, the overall probability of a fusion reactionis increased significantly.

As an example, the electron-rich region may be characterized by anycombination of the following parameter values:

Density of free electrons: about 10²³/cm³

Density of neutrals: about 10²⁰/cm³

Density of positive ions: about 10¹⁵-10¹⁶/cm³ (about 10⁻⁵ to 0.01% ofneutrals)

Difference in densities of electrons and positive ions: about 10⁶ to10⁸/cm³

Thickness (radial) of free electron-rich region (region where most ofthe electron density gradient exists): about 1 micrometer

Electric field strength in the electron-rich region: about 10⁶ to 10⁸V/m

Electron temperature: about 1800-2000 K. (about 0.15 to 0.17 eV)

Centripetal acceleration: about 10⁹ g's (where g is the acceleration dueto gravity=9.8 ms⁻²)

The free electrons in such systems may be viewed as collectivelycatalyzing the fusion reaction of two nuclei. By analogy, one or moremuons in association with protons and deuterons are sometimes describedas catalyzing the fusion of hydrogen and deuterium atoms. Just as muonscatalyze the fusion by allowing two fusing nuclei to get closer to oneanother, the free electrons in the vicinity of fusing nuclei catalyzefusion reactions described herein. Effectively, the electrons reduce theenergy barrier that prevents the two reactants from coming close enoughto react. This is very similar to the action of any catalyst in achemical or physical context. Both muons and electrons increase the rateof reaction but do not actually participate in the reaction; they simplyreduce the energy barrier required to bring the reactants in closeenough proximity to react.

However, muon and electron catalysis have few other similarities. Muoncatalyzed fusion is not commercially viable for various reasons.Notably, muons have a much greater mass than electrons and henceproducing them is much more energetically expensive. Further, onlyrelatively few of them can be produced at any instant in time, whichmeans the breakeven requirement for fusion is not attainable. For theproton-boron-11 reaction, breakeven fusion may require approximately10¹⁷ successful fusion interactions per cubic centimeter per second.Only a few nuclei in a large pool would be able to benefit from muoncatalyzed fusion, nowhere near the level needed to support fusion.

In contrast, electrons can be easily produced, and in high density. Forexample, in accordance with the techniques disclosed herein, electronscan be generated at densities of approximately 10²⁰ per cubic centimeteror greater. With such high densities, the electrons act collectively toproduce a high electric field, which over a relatively large volumereduces the Coulombic barrier to interaction between approaching nuclei.Such a relatively large volume permits the needed interactions tobreakeven, i.e. at least about 10¹⁷ successful fusion interactions percubic centimeter per second.

Terminology

A “reactor” is an apparatus in which one or more reactants react toproduce one or more products, often with an accompanying release ofenergy. The one or more reactants are provided in a reactor bycontinuous delivery, intermittent delivery, and/or a one-time delivery.They may be provided in the form of gases, liquids, or solids. In somecases, a reactant is provided as a component of a reaction; for example,it may be included in a structure of the reactor such as a wall. Boron11, lithium 6, carbon 12, and the like may be provided in a confiningwall of a reactor. In some cases, a reactant is provided from anexternal source such as from a gas supply tank. In certain embodiments,the reactor is configured to promote a nuclear fusion reaction having aQ>1. A reactor may have components for removal of products and/or energyproduced during the reaction. Product removal components may be ports,passages, getters, and the like. Energy removal components may be heatexchangers and the like for removing thermal energy, inductors andsimilar structures for directly removing electrical energy, etc. Thereactor components may permit products and energy to be removedcontinuously or intermittently. In certain embodiments, a reactor hasone or more confining walls that contain the reactants, and in somecases, provides a source of reactant, an electrical field, etc. Asillustrated throughout this disclosure, reactors suitable for providinga sustained fusion reaction may have many different designs.

A “rotor” is a reactor or reactor component in which one or morereactant or product species (particles) rotates in a space. The spacemay be defined at least in part by a confining wall as described herein.In some cases, the rotation is induced by a magnetic force, anelectrical force, and/or a combination of the two, as in the case of aLorentz force. In certain embodiments, the rotation is induced byapplying an electrical and/or magnetic force to electrically chargedparticles in a manner that causes them to rotate in a confinementregion; the rotating charged particles collide with neutrals to causethe neutrals to likewise rotate in the confinement region, a phenomenonsometimes called ion-molecule coupling. Because the neutrals are notaffected by the electrical and/or magnetic force, they would not rotatein the confinement region absent the interaction with the chargedparticles. The confining wall or other outer structure of the rotor mayhave many closed shapes as described herein. In some embodiments, theouter structure has a generally or substantially circular or cylindricalshape. In such cases, the shape need not be geometrically exact, but mayexhibit certain variations such as eccentricity around an axis ofrotation, non-continuous curvature such as vertices, and the like.

In some cases, the confinement region of a rotor has an interior rod orother structure arranged concentrically with respect to the confiningwall. In such cases, the rotor has an “annular space” where theparticles rotate. When used herein, an “annular space” refers to aconfinement region wherein the region is substantially ring-shaped. Itshould be understood that some rotors do not have an interior rod orother structure to define an annular space. In such cases, theconfinement region of the rotor is simply a hollow structure. While anannular space may have a generally cylindrical shape, such a shape mayexhibit certain variations such as eccentricity around an axis ofrotation, non-continuous curvature such as vertices, and the like.

The “Lorentz force” is provided by a combination of electric andmagnetic forces on a charge due to the resulting electromagnetic fields.The magnitude and direction of the force is given by the cross productof the electric and magnetic fields; hence the force is sometimesreferred to as J×B. When the electric and magnetic fields haveorthogonal directions, the force applied to a charged particle has arotational direction that may be represented by the right-hand rulemnemonic.

In fusion reactions, participating reactants and products, which mayinclude protons, alpha particles, and boron (¹¹B), are not necessarilypresent in complete purity. To the extent that any such reactant,product, or other component of a reaction is presented herein, suchcomponent is understood to be substantially present. In other words, thecomponent need not be present at the level of 100% but may be present ata lower level, e.g., about 95% by mass or about 99% by mass.

An aneutronic reaction is conventionally understood to be a fusionreaction in which neutrons carry no more than 1% of the total releasedenergy. As used herein, an aneutronic reaction or a substantiallyaneutronic reaction is one that meets this criterion.

Examples of aneutronic reactions include:

p+B¹¹→3He⁴+8.68 MeV

D+He³→He⁴+p+18.35 MeV

p+Li⁶→He⁴+He³+4.02 MeV

p+Li⁷→2He⁴+17.35 MeV

p+p→D+e⁺+v+1.44 MeV

D+p→He³+γ+5.49 MeV

He³+He³→He⁴+2p+12.86 MeV

p+C¹²→N¹³+γ+1.94 MeV

N¹³→C¹³+e⁺+v+γ+2.22 MeV

p+C¹³→N¹⁴+γ+7.55 MeV

p+N¹⁴→O¹⁵+γ+7.29 MeV

O¹⁵→N¹⁵+e⁺+v+γ+2.76 MeV

p+N¹⁵→C¹²+He⁴+4.97 MeV

C¹²+C¹²→Na²³+p+2.24 MeV

C¹²+C¹²→Na²⁰+He⁴+4.62 MeV

C¹²+C¹²→Mg²⁴+γ+13.93 MeV

Examples of neutronic reactions include

D+T→He⁴+n+17.59 MeV

D+D→He³+n+3.27 MeV

T+T→He⁴+2n+11.33 MeV

The coulombic repulsion force is the electrostatic force experienced bytwo or more particles of the same charge. For two interacting particles,it is proportional to the reciprocal of the square of the separationdistance (Coulomb's law). Thus, the repulsion becomes significantlystronger as charged particles approach one another. The repulsive forceexperienced by a charged particle in an electric field produced bymultiple charged particles is given by the superposition of thecontributions of all charged particles in the vicinity.

Lowering the coulombic barrier means that the commonly known andunderstood coulombic repulsion force typically calculated or experiencedbetween two isolated particles is “lowered” or reduced by somecalculable degree when the particles are in some proximity to asufficient number of electrons or other charged particles to reduce therepulsive force that isolated particles would otherwise experience. Asan example, the presence of excess electrons at a density of XX reducethe coulombic repulsive force between two positively charged YYparticles in the domain of the electrons by ZZ %.

Lorentzian Rotor Embodiments First Embodiment

FIGS. 1a-c depict a first embodiment of a reactor in which chargedparticles, charged species, or ions are rotated by the Lorentz force.FIG. 1a is a cross-section view of a reactor, while FIG. 1b provides anisometric cutout view of the same reactor along of section A-A from FIG.1a . Unless stated otherwise, directionality using the r, Θ, and zcoordinates pertains to a cylindrical coordinate system as shown in FIG.1b . In the depicted embodiment, a Lorentzian driven rotor has outerwall 110, which also serves as the outer electrode, and concentric innerelectrode 120, sometimes referred to as a discharge rod, that isseparated from the outer electrode by annular space 140. An electricfield is formed across the annular space by applying an electricpotential between the inner electrode 120 and the shroud 140. When asufficient electric potential is applied between the electrodes, aportion of the gas in the annular space is ionized, and a radial plasmacurrent across the annular space is generated. In various embodiments,the inner electrode is held at a high positive potential while theshroud is grounded such that the electric field, and the flow ofcurrent, is substantially in the positive r-direction.

FIG. 1c depicts how the Lorentzian force is used to drive chargedparticles azimuthally within the confining wall 110. In FIG. 1c , thedischarge rod has been removed and the axis has translated in thez-direction to improve clarity. While not shown, a magnet such as apermanent magnet or a superconducting magnet is used to generate anapplied magnetic field that is substantially parallel to the z-axis(substantially axial direction) within the annular space. The magneticfield is substantially perpendicular to the direction of the electricalcurrent causing the moving charged particles, charged species, and ionsto experience a Lorentz force in the azimuthal (or Θ) direction. Forexample, consider the case in which the discharge rod has a positivepotential vis-à-vis the outer electrode (e.g., the discharge rod has anapplied positive potential while the outer electrode is grounded),thereby producing an electric field in the r-direction (144). In thisconfiguration, positively charged ions will move in the r-directiontowards the outer electrode through the annular space 140. If a magneticfield concurrently points in the z-direction (146), the ions willexperience a Lorentz force in the −Θ direction, or clockwise directionas viewed from the perspective shown in FIGS. 1b and 1c . In some casesthe electric field and magnetic field may be at an angle that differsfrom the perpendicular yet is not parallel, such that perpendicularcomponents, to a lesser or greater extent, are present in sufficientstrength to create a sufficiently strong azimuthal Lorentz force. Thisazimuthal force acts on charged particles, charged species, and ions,which in turn couple with neutrals such that neutrals in the annularspace between the central discharge rod and outer electrode also aremade to move at high rotational velocity. The lack of any movingmechanical parts means that there is little limitation to the speed atwhich rotation can occur, thus providing rotation rates of neutrals andcharged particles that are in excess of, for example, 100,000 RPS.

Reverse Electrical Polarity Embodiment

FIGS. 5a-d depict another embodiment in which a reactor may utilize aLorentzian force to drive ions and neutrals, through ion-neutralcoupling, into rotation. Reactors configured for reverse electricalpolarity differ from the reactors depicted in FIGS. 1a-c in that theelectric field, and the flow of current (by convention in the directionof positive charge movement), is substantially in the negativer-direction. FIG. 5a is a cross-section view of a reactor, while FIG. 5bprovides an isometric cutout view of the same reactor along of sectionA-A from FIG. 5a . A reverse electrical polarity rotor has outerelectrode 510 and concentric inner electrode 520 that is separated fromthe outer electrode by annular space 540, sometimes referred to hereinas a confinement region. A radial electric field directed towards theinner electrode may be formed in the annular space by applying anelectric potential to the inner electrode and/or the outer electrode.When a sufficient electric potential is applied between the electrodes,a portion of the gas in the annular space is ionized, and a radialplasma current across the annular space is generated.

FIG. 5c depicts how the Lorentzian force is used to drive chargedparticles azimuthally within the reactor. In FIG. 5c , the innerelectrode has been removed from view, and the depicted axis has beentranslated in the z-direction to improve clarity. While not shown, amagnet such as a permanent magnet or a superconducting magnet is used togenerate an applied magnetic field that is substantially parallel to thez-axis (i.e., in a substantially axial direction) within the annularspace. The magnetic field is substantially perpendicular to thedirection of the electrical current causing the moving chargedparticles, charged species, and ions to experience a Lorentz force inthe azimuthal (or Θ) direction. For example, consider the case in whichthe inner electrode has an applied negative potential while the outerelectrode is grounded (or held at a positive potential) producing anelectric field in the negative r-direction (544). In this configuration,positively charged ions will move in the negative r-direction towardsthe inner electrode through the annular space 540. If a magnetic fieldconcurrently points in the z-direction (546), the ions will experience aLorentz force in the +Θ direction or counterclockwise direction asviewed from the perspective shown in FIGS. 5b and 5c . In some cases,the electric field and magnetic field may be at an angle that differsfrom the perpendicular yet is not parallel, such that perpendicularcomponents, to a lesser or greater extent, are present in sufficientstrength to create a sufficiently strong azimuthal Lorentz force. Thisazimuthal force acts on charged particles, charged species, and ions,which in turn couple with neutrals such that neutrals in the annularspace are also made to move at high rotational velocity. The lack of anymoving mechanical parts means that there is little limitation to thespeed at which rotation can occur, thus providing rotation rates ofneutrals and charged particles that are in excess of, for example,100,000 RPS.

Reverse Fields Embodiment

FIGS. 6a-d depict multiple views of another reactor embodiment thatutilizes a Lorentzian force to drive ions and neutrals, throughion-neutral coupling, into rotation. The reactor of this embodimentoperates using a reverse fields configuration. Reactors having thisconfiguration differ from the reactors depicted in FIGS. 1a-c and FIGS.5a-d in that the orientation of the electric field and the magneticfield within the confinement region are reversed. In this configuration,the magnetic field, instead of being substantially parallel to thez-axis, is directed radially in the positive or negative r-direction.Similarly, the electric field, rather than being directed radially, issubstantially parallel to the z-axis. FIG. 6a is an isometric view ofthe reactor, FIG. 6b is a view of the reactor in the z-direction, FIG.6c is an isometric section view of the reactor (corresponding to lineA-A in FIG. 6b ), and FIG. 6d provides a side view of the reactor. Thedepicted embodiment includes an inner ring magnet 626 and a concentricouter ring magnet 616 that also serves as the confining wall. The ringmagnets have their poles oriented in the same direction, such thatcorresponding surfaces of the inner and outer ring magnets are the same.In this case, the exterior surface is a north pole 658, and the interiorsurface is a south pole 659. In some embodiments, there may be one ormore additional layers of material on the interior surface of magnet 658such that the confining surface material is different from the magneticmaterial. The region between concentric magnets forms the annular space640 which is bound in the z-direction by electrodes on one end of theconfinement region 660 a and electrodes on the other end of theconfinement region 660 b. Generally, all the electrodes on either sideof the confinement region (corresponding to electrodes 660 a or toelectrodes 660 b) are given a similar electric potential. Unlike in thedepicted hybrid reactor, electrodes 660 a (or to electrodes 660 b) maybe a single contiguous electrode forming, for example, a ring or a diskshape. If electrodes 660 a are grounded and electrodes on the other sideof the annular space 660 b are given a positive potential then anelectric field is applied through the confinement region in the positivez-direction. If the magnetic field points in the r-direction (asdepicted) the orthogonal electric and magnetic fields cause ions torotate azimuthally in the Θ direction (see, e.g., FIG. 6c ).Alternatively, if an electric field was pointed in the negativez-direction by applying a positive potential to electrodes 660 a whilegrounding electrodes 660 b, ions would rotate in the −Θ direction.

Wave-Particle Embodiments

A second embodiment of a controlled fusion device is shown in FIGS. 7aand 7b in which ions rotate as a result of oscillating electrostaticfields. In this embodiment ions are accelerated azimuthally by electricfields produced from multiple discrete wall electrodes 714 located on,or forming, an outer ring, optionally in combination with interiorelectrodes 724 located on, or forming, an inner ring to generatelocalized, azimuthally-varying electric fields within an annular space740. In some cases, the wall electrodes collectively form the confiningwall, and in some cases, the wall electrodes may be disposed on orwithin a portion of a confining wall or scaffold. The electric fieldadvances azimuthally in a controlled sequence such that theelectrostatic force applied to ions proceeds sequentially in asubstantially azimuthal direction (in the Θ or −Θ direction). In thisway, charged species are accelerated akin to a Maglev train that ispropelled by oscillating magnetic fields along a train track. Anoscillatory potential may be applied to the electrodes. The oscillationsmay vary in phase or other parameter from one electrode to the next toinduce or maintain rotational movement of ions.

Ions present in the annular space experience an electrostatic force as aresult of electric fields, and only a relatively small number orpercentage of ions are needed to drive large numbers or percentages ofneutrals through the principle of ion-neutral coupling. Ions used todrive the neutrals into rotation may be generated by any suitablemechanism such as inductive or capacitive coupling. In some embodiments,ions are generated when an RF charge sequence is applied to the walland/or interior electrodes. In some embodiments the wall and/or interiorelectrodes may first undergo an initial charge sequence to ionize someof the neutral gas in the annular space and then transition to adifferent charge sequence that drives the rotation of ions. For example,a charge profile used to ionize a gas might simply involve grounding theconfining wall electrodes 714 while applying a high potential to theinterior electrodes 724. In some embodiments, a gas that is alreadypartially ionized may be introduced into the annular space 740.

While FIGS. 7a and 7b depict two binary charge profiles that may be usedto drive ion rotation in the annular space, many alternative chargesequences are possible. In some charge sequences, an electrode may be,for instance, held at a ground potential for a duration of time or mayhave a charge sequence that is asymmetrical (e.g., a positive potentialis held for twice the duration of a negative potential).

In certain embodiments, this system does not require a magnetic fieldsuch as an axial static magnetic field. FIG. 7a depicts an example ofthis embodiment taken at a first point in in time when the electrodesare provided with a first potential profile such that ions (e.g., acloud or a grouping of ions) 704 experiences a force in the −Θ̂direction. FIG. 7b depicts the embodiment of FIG. 7a at a later point intime when the electrodes are provided with a different potential profilesuch that ions 704 continue to experience an azimuthal force in the −Θdirection.

Hybrid Embodiments

In certain embodiments, a reactor includes features for producing bothLorentzian force and an oscillating electrostatic field to drive ionsand neutrals, through ion-neutral coupling, into rotation. At any stageof operation, the reactor may use one or both of these mechanisms. FIGS.6a-f depict an example reactor suitable for such operation. FIG. 6a isan isometric view of the reactor, FIG. 6b is a view of the reactor inthe z-direction, FIG. 6c is an isometric section view of the reactor(corresponding to line A-A in FIG. 6b ), FIG. 6d provides a side view ofthe reactor, and FIGS. 6e and 6f are section views (corresponding toline B-B in FIG. 6d ) at different points in time. The depictedembodiment includes an inner ring magnet 626 and a concentric outer ringmagnet 616 that also serves as the confining wall. The ring magnets havetheir poles oriented in the same direction, such that correspondingsurfaces of the inner and outer ring magnets are the same. In this case,the exterior surface is a north pole 658, and the interior surface is asouth pole 659. In some embodiments, there may be one or more additionallayers of material on the interior surface of magnet 658 such that theconfining surface material is different from the magnetic material. Theregion between concentric magnets forms the annular space 640 which isbound in the z-direction by one or more pairs of electrodes 660 a and660 b. When electrode pairs 660 a and 660 b are given differentpotentials, an electric field substantially parallel to the z-directionis generated in the annular space, for example, by applying a positivepotential to electrodes 660 a while grounding electrodes 660 b. Whenions are generated in the annular space, the orthogonal electric andmagnetic fields cause them to rotate azimuthally in the −Θ direction(see, e.g., FIG. 6c ). If a positive potential were applied toelectrodes 660 b while electrodes 660 a were grounded, ions would rotatein the Θ direction.

In some embodiments, as depicted in FIGS. 6a-e , a plurality ofelectrodes 660 a and 660 b are distributed radially along the annularspace. In such cases, the reactor may be driven in a fashion similar tothat of the reactor in FIGS. 7a and 7b . During operation, eachelectrode pair is driven with a substantially similar electric potentialthat differs from the potential of an adjacent electrode pair such thata localized electric field is generated in the Θ direction. As depictedin FIGS. 6d and 6e , the voltages applied to electrode pairs can bemodulated in a controlled sequence so that the electrostatic forceapplied to ions presents a substantially continuous azimuthally (in theΘ or −Θ direction) varying component. In some configurations, a reactormay be configured to operate in a manner that initially drives ions andneutrals by a Lorentzian force and then transitions to driving ions andneutrals using the just described alternating electrostatic fields.6.

Reactor Types (Sizes)

In one aspect, reactors may be classified into groups by the poweroutput they provide. In this manner reactors of the present disclosureare, for purposes of this discussion, divided into small, medium andlarge-scale reactors. Small scale reactors are typically capable ofgenerating between about 1-10 kW of power. In some embodiments, thesereactors are used for personal applications such as powering automobilesor providing power to a household. The next classification is mediumscale reactors which typically deliver between about 10 kW-50 MW ofpower. Medium scale reactors may be used for larger applications such asserver farms, and large vehicles such as trains, and submarines. Largescale reactors are reactors that are designed to output between about 50MW-10 GW of power and may be used for large operations such as poweringportions of a power grid and/or industrial power plants. While thesethree general classifications provide practical categories to which thepresent disclosure may relate, reactors disclosed herein are not tied toany of these categories.

The surface area (product of the perimeter and axial direction) of ashroud or confining wall typically limits the maximum power that may begenerated by a reactor. A shroud having a large surface area supportsfusion reactions over the large area of an interior surface (e.g., 122in FIG. 1a ). For small-scale reactors, the radius of the interiorsurface of the shroud is typically about 1 centimeter to about 2 metersand the surface area of the interior surface is typically between about5 cm³ and 20 cm³. For a medium scale reactor, the radius of the interiorsurface of the shroud is typically about 2 m to about 10 m and thesurface area of the interior surface is typically between about 25 m³and 150 m³. For a large scale reactor, the radius of the interiorsurface of the shroud is typically about 10 meters to about 50 metersand the surface area of the interior surface is typically between about125 m³ and 628 m³. In some cases the radius of the interior surface maybe on the order of kilometers, having a similar footprint to the LargeHadron Collider (LHC) run the CERN laboratory in Switzerland. Each ofthe above values assumes a single reactor that stands alone or is partof a contiguous stack of reactors (described below).

First Embodiment

FIGS. 1a-c depict the structure of a reactor having concentricelectrodes that utilizes a Lorentzian rotor to drive charged particlesand fusion reactants into rotation. This embodiment has an innerelectrode 120, an outer electrode 110, and an annular space 140 betweenthe two electrodes. During operation, an applied potential between theseelectrodes creates an electric field 144 that is substantially in ther-direction. While not shown, this embodiment also includes permanentmagnets or an electromagnet (e.g., a superconducting magnet) thatgenerates a magnetic field 146 in the z-direction between the inner andouter electrodes. As depicted in FIG. 1c , charged particles movingbetween the electrodes experience an azimuthally directed force, or aLorentzian force, as a result of the radial electric field and the axialmagnetic field.

As shown, the reactor depicted in FIG. 1a has a gap 142 that radiallyseparates the outer surface of the inner electrode 112 and the interiorsurface of the outer electrode 122. While the surface areas of thefacing surfaces of the inner and outer electrodes may dictate the scaleof a reactor, the radial gap may remain relatively constant across awide range of applications. In some cases, the upper limit of a gap maybe limited by the power available to ionize gas in the annular space andgenerate a plasma current, while the lower limit of the gap may belimited to manufacturing tolerances. When a gap is very small, e.g. lessthan 0.1 mm, any misalignment between the electrodes may cause theelectrodes to touch creating a short circuit. Of course, asmanufacturing tolerances allow greater precision, smaller gaps may befeasible. In some embodiments, the gap may be between about 1 mm andabout 50 cm, and in some embodiments, the gap may be between about 5 cmand about 20 cm. In some cases, the gap may vary along the r-directionand/or the z-direction of a reactor. For example, the radius of theinner electrode may vary as a function of position along the z-axiswhile the radius of the inner surface of the outer electrode isconstant.

The length in the z-direction of the confining wall created by the outerelectrode may be determined by the radial dimensions and the powergeneration requirements of the reactor. In some embodiments, the lengthof the outer electrode in the z-direction may be limited by the type andconfiguration of magnets used to create the magnetic field. For example,if permanent magnets are placed on either end of the annular space alongthe z-direction (as depicted in FIG. 11), the outer electrode may belimited to about 5 or about 10 cm in the z-direction. If, however, themagnetic field is generated using multiple permanent ring magnets, asshown in FIGS. 16 and 17, or an electromagnet or a superconductingmagnet, as shown in FIG. 10, the length of the outer electrode in thez-direction may be much longer. For example, the outer electrode may bebetween about 1 meter and about 10 meters. Generally, the outerelectrode 110 is of a similar length to the inner electrode 120,however, this need not always be the case. In some embodiments, theinner electrode may extend beyond the outer electrode in one or bothdirections. In some embodiments, the length of the outer electrode mayexceed the length of the inner electrode such that the outer electrodeextends beyond the inner electrode in one or both directions.

While FIGS. 1a-1b depict one configuration in which a solid, circularinner electrode is used in conjunction with circular outer electrodes,there are many permutations of electrode shapes that may be used in thisconfiguration. Several non-limiting examples of alternate embodimentswill be apparent to those of skill in the art and are discussed withreference to FIGS. 8a-b and FIGS. 9a-c . While several illustrativeexamples are provided, one can easily understand how many additionalelectrode shapes are feasible.

As depicted in FIG. 8a , in some embodiments the inner electrode 820 maybe a ring-like structure that is not solid all the way through.Providing a cavity or an open space within the inner electrode may beuseful for heat dissipation, the use of internal magnets such shown inFIGS. 17a-c , or the use of other components within the reactor. In somecases, the radius of the inner and outer electrodes may vary along thez-direction of a reactor. For example, as shown in FIG. 8a , an innerelectrode 820 may have a larger circumference at some locations alongthe z-direction, reducing the gap 842 at those locations. Conversely, auniform inner electrode may be used with an outer electrode having aninner radius that changes or even fluctuates along the z-direction. Insome instances, such as the embodiment depicted in FIG. 8b , both theradius of the inner electrode 820 and the radius on the inner surface ofthe outer electrode 810 vary in the z-direction such that the gap 842 ismaintained along the z-direction of the reactor.

FIGS. 9a-c depict cross sections of reactors that have non-circularcross sections. As depicted, in some embodiments, the inner electrode920, and the outer electrode 910 may have a radius that variesazimuthally, i.e., in the Θ direction. In some cases, the surfaces ofthe inner and outer electrodes (912 and 922) may have an ellipticalcross section as shown in FIG. 9a . In some cases, the major and minoraxis of an ellipse-shaped cross section electrode may only be off by asmall percentage, for example, less than 1%. In some embodiments surface912 and/or 922 may form a polygonal cross section, such as the reactorshown in FIG. 9b having a cross section that forms a heptagon. In someembodiments surfaces 912 and 922 may have 4 or more sides; in someembodiments more than 8 sides, and in some embodiments more than 16sides. Having corners on surface 912 may be advantageous in certainsituations; for example, rotating particles may have an increased rateof collisions with target materials at corner locations resulting in anincreased rate of fusion. In some embodiments, such as in the reactorconfiguration depicted in FIG. 9c , the radius of the inner or outerelectrodes, defined by surfaces 912 and 922, may vary in the Θ directionsuch that the cross section of either surface has a patterned edge;e.g., an edge that is sinusoidal, saw-tooth shaped, or square-waveshaped. While the inner and outer electrodes in the depicted embodimentsare co-axial, in some embodiments the axes of the inner and outerelectrodes are offset, e.g., the annular space is eccentric, such thatthe inner and outer electrodes have z-direction axes that aresubstantially parallel but not collinear.

Materials for inner and outer electrodes may depend on the reactor size,selected fusion reactants, and other parameters that govern theoperation of a fusion reactor. In general, there are many trade-offssuch as ranges in cost, thermal properties, and electrical propertiesthat determine which materials are selected for reactors. Refractorymetals (e.g., tungsten and tantalum) may be chosen for small scalereactors because of their extremely high melting points and relativelyhigh electrical conductivity at high temperatures; however using thesematerials in a large scale reactor may significantly increase the costof a reactor.

In certain embodiments, the electrode materials have a sufficiently highmelting temperature to withstand the thermal energy released duringoperation of the reactor. For the outer electrode, forming the confiningwall on which fusion reactions may occur, the thermal energy release isoften great. To withstand regular use, the material of the outerelectrode should have a melting temperature that is in excess oftemperatures reached by the electrodes during operation of the reactor.In some cases the material chosen for an electrode is greater than about800° C., in some cases, the melting temperature of an electrode isgreater than about 1500 C, and in other cases the melting temperature isgreater than about 2000° C.

In many embodiments, it is beneficial for the electrode material to havea high thermal conductivity. If heat can be extracted from an electrode(e.g., using a heat exchanger) at an equivalent rate to which heat isintroduced to the electrode during steady state conditions, then areactor may be suitable for continuous operation. When an electrodematerial has a high thermal conductivity, the rate at which heat beextracted may be improved and concerns of overheating are reduced. Insome cases the thermal conductivity is greater than about

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in some cases the thermal conductivity is greater than about

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and in some cases the thermal conductivity is greater than about

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In certain cases, such as when a reactor is configured for pulsedoperation, it may be beneficial for the electrode material to have ahigh heat capacity. By having a high heat capacity, an electrodeincreases in temperature at a slower rate during operation of thereactor. When used in a pulsed operation, the generated thermal energymay continue to be dissipated through the electrodes between pulses,preventing the electrodes from reaching their melting temperature. Insome cases the specific heat of the electrode should be higher thanabout 0.25 J/g/° C., in some cases, the specific heat should be greaterthan about 0.37 J/g/° C., in other cases, the specific heat should behigher than about 0.45 J/g/° C.

In certain embodiments, the electrode material has a relatively smallcoefficient of thermal expansion. In some cases, by having a lowcoefficient of thermal expansion a reactor may have improved performanceover a greater range of temperatures. For example, if a reactor has agap that is about 1 millimeter at room temperature, the gap may beproportionally much smaller during steady state operation due to theexpansion of the inner and/or outer electrodes. If a thermal coefficientis too high, the outer and inner electrodes may touch causing a shortcircuit. Alternatively, if a reactor is designed to have a certain gapat operating temperatures, the gap may be larger than desired when areactor is first turned on. In some cases the linear coefficient ofthermal expansion of an electrode material is less than about 4.3×10⁻⁶°C.⁻¹, in some cases the linear coefficient of thermal expansion of anelectrode material is less than about 6.5×10° C.⁻¹, and in other casesthe linear coefficient of thermal expansion of an electrode material isless than about 17.3×10⁻⁶° C.⁻¹.

To facilitate reactor operation, the electrodes may be designed to havemechanical properties such as resistance to degradation during thermalcycling. Under certain conditions, some materials, e.g. stainlesssteels, become brittle and eventually experience fatigue as a result ofthermal cycling. If a reactor operates in pulsed operation and anelectrode is rapidly heated and cooled, internal stress may develop. Insome cases, the effects of thermal loading cycles may be reduced byusing an electrode having a single bulk material, or by using two ormore materials having similar coefficients of expansion. Certainmaterials may experience deformation due to creep at high temperatures.Thus electrode materials may be chosen to maintain their strength atelevated temperatures.

Electrode materials may be chemically inert and not significantlyaffected by oxidation, corrosion, or other chemical degradation over thelifetime of a reactor. Another consideration for electrode materials iswhether or not they are ferromagnetic. In some cases, if ferromagneticmaterials are used, internal localized magnetic fields are created thatmay interfere with establishment or maintenance of the intended magneticfield within the annular space.

In a Lorentzian driven reactor having concentric electrodes, the innerand outer electrodes may be made from a material that is sufficientlyconductive such that, during operation, an electric potential is evenlyapplied over the surfaces of the electrodes. In certain embodiments, atroom temperature, the resistivity of the inner or outer electrodematerial is less than about 7×10⁻⁷ Ωm, and in some cases less than about1.68×10⁻⁸ Ωm. In addition to being conductive at room temperate, when areactor is not in operation, the inner and outer electrodes may beconductive at higher operating temperatures. During operation the inneror outer electrode may reach temperatures of between about 600° C. toabout 2000° C. During operation, the resistivity of the outer electrodematerial should be no greater than about 1.7E-8 Ωm, and in some cases nogreater than about 1E-6 Ωm.

In cases where reactants or by-products include hydrogen or helium,consideration may be given to a material's resistance to hydrogenembrittlement. Hydrogen embrittlement is a process by which metals suchas stainless steel become brittle and in some cases fracture due to theintroduction and subsequent diffusion of hydrogen atoms or moleculesinto the metal. Since the solubility of hydrogen increases at highertemperatures, the diffusion of hydrogen into the electrode material mayincrease during operation of the reactor. When assisted by aconcentration gradient in which there is significantly more hydrogenoutside the metal than inside, e.g., caused by the centrifugaldensification of hydrogen atoms that impinge on the confining wall, thediffusion rates may be increased further. Individual hydrogen atomswithin the metal gradually recombine to form hydrogen molecules,creating an internal pressure in the metal. Additionally, oralternatively, entrained hydrogen molecules themselves create internalpressure. This pressure can increase to levels where the metal hasreduced ductility, toughness, and tensile strength, up to the pointwhere cracks form and the electrode fails. In some cases, in which ametal contains carbon (e.g. carbonized steel) an electrode may besusceptible to a process known as hydrogen attack in which hydrogenatoms diffuse into the into the steel and recombine with carbon to formmethane gas. As methane gas collects within the metal, it generatesinternal pressure that may lead to mechanical failure of the device.While methods for reducing the effects of the hydrogen embrittlement aredescribed elsewhere herein, in general, a material's susceptibility toembrittlement is considered when designing electrodes. In some cases,electrodes may include platinum, platinum alloys, and ceramics such asboron nitride, each of which resist hydrogen embrittlement. In somecases, the metallurgical structure may be modified so that the effect ofhydrogen in the lattice of a metal is less detrimental. For example, insome cases, a metal or metal alloy may undergo a heat treatment toachieve a desired metallurgical structure.

In various embodiments, the inner and outer electrodes are primarilyconstructed of metals and metal alloys. In some embodiments, the innerand/or outer electrode is made at least in part from a refractory metalhaving a high melting temperature. Refractory metals are known for beingchemically inert, suitable for fabrication using powder metallurgy, andare stable against creep at very high temperatures. Examples of suitablerefractory metals include niobium, molybdenum, tantalum, tungsten,rhenium, titanium, vanadium, chromium, zirconium, hafnium, ruthenium,rhodium, osmium and iridium. In one example, at least the outerelectrode includes tantalum.

In some embodiments, one or both electrodes are made using stainlesssteel. Benefits of stainless steel include its machinability andresistance to corrosion. In some cases, electrodes are made at least inpart from a non-carbon based stainless steel, such as Incoloy, which maybe more resistant than carbonized stainless steels to hydrogenembrittlement. In some cases, an electrode may be made at least in partof a nickel alloy that maintains its strength at very high temperaturessuch as Inconel, Monel, Hastelloys, and Nimonic. In some cases,electrodes are made at least in part from copper or a copper alloy. Insome cases, an electrode is configured with one or more channels forinternal cooling to extract heat, such that materials with lowerresistance to extreme temperatures may be used.

While absorption of a small atom fusion reactant such as hydrogen,deuterium, or helium may lead to a mechanical failure of an electrode,under some operating conditions, deleterious embrittlement effects maybe reduced or eliminated for certain materials. For example, under someconditions hydrogen absorbing materials such as palladium-silver alloysappear to be impervious to hydrogen embrittlement (Jimenez, Gilberto, etal. “A comparative assessment of hydrogen embrittlement: palladium andpalladium-silver (25 weight % silver) subjected to hydrogenabsorption/desorption cycling” (2016), which is incorporated herein byreference in its entirety). In such cases, absorption of a fusionreactant may increase the rate of a fusion reaction, for example, arotating gas reactant such as hydrogen may collide with a fixed hydrogenatom fixed on the outer electrode (or the confining wall). In somecases, reactants are provided to the reactor by diffusing reactantsthrough the inner and/or the outer electrode. In some cases, anelectrode may include titanium, palladium, or a palladium alloy for thepurpose of delivering fusion reactants or increasing the rate ofcollisions between fusion reactants.

In some cases, as discussed elsewhere herein, an outer or innerelectrode may include an electron emitting material having a highelectron emissivity. In some cases, an outer electrode may include atarget material that includes a fusion reactant. In some cases, thetarget material is consumed during operation as a result of a fusionreaction. For example, in some cases, lanthanum hexaboride is used as atarget material, and boron-11 atoms are consumed during a proton-boronreaction.

First Embodiment—Electrodes

In some embodiments the outer electrode is monolithic, being made from asingle material, and in other embodiments, the outer electrode has alayered or segmented structure including two or more materials. In someembodiments, the interior surface of the outer electrode, the confiningwall, includes a target material (a material containing a fusionreactant), or an electron emitting material. In some cases, a targetmaterial or an electron emitter may cover the entire surface area of theconfinement wall, and in some cases, a target material or electronemitter is located at one or more discrete locations along theconfinement wall (e.g., as depicted by the electron emitters in FIGS.21a-b ).

In some cases, an inner layer of the outer electrode provides oneproperty while a more exterior layer provides a different property. Forexample, an interior layer that forms the surface of the confinementwall may have a high melting temperature, while an exterior layer mayhave a superior thermal conductivity or electrical conductivity.

In some cases, an electrode may include a layer of material forming theconfinement wall that has a higher resistance to hydrogen embrittlementthan the rest of the electrode. In some cases, an electrode includes aceramic coating that can prevent hydrogen atoms from penetrating intothe lattice of the outer electrode or provide thermal insulation of thebulk electrode material. In some embodiments, an outer electrode mayhave a layer of aluminum nitride, aluminum oxide, or boron nitride. Somematerials that have a low electrical conductivity at room temperature(e.g. boron nitride) may be heat treated to improve their electricalconductivity. In some cases, an electrode may undergo a surfacetreatment that adds material to the electrode surface and reduceshydrogen embrittlement. For example, when an electrode is made out of amaterial that is susceptible to hydrogen embrittlement (e.g., tantalum),embrittlement may be reduced by adding minor amounts of a noble metal tothe electrode surface. In some cases, the noble metal may only cover asmall portion of the electrode surface. For example, the noble metal maycover less than about 50%, less than about 30%, or less than 10% of theelectrode surface while providing a significant reduction of hydrogenembrittlement to the electrode. In some cases, small amounts ofplatinum, palladium, gold, iridium, rhodium, osmium, rhenium, andruthenium may be added to an electrode surface to reduce hydrogenembrittlement. In some cases, small spots (e.g., about 0.5 inches indiameter) of noble metal may be riveted or welded to the electrodesurface. In some cases, a noble metal powder may be added to a reactor,and during normal operation, the powder is sputtered onto the electrodesurface. In some cases, a nobel metal may be periodically added to thesurfaces of electrodes, e.g., after reactor has operated for apredetermined amount of time.

In some cases, a sleeve is attached to the interior surface of the outerelectrode, such that the interior surface of the sleeve forms theconfinement wall. In some cases, a sleeve may be used to, e.g., providea target material, provide an electron emitter, provide a barrier forhydrogen penetration into the outer electrode, and/or provide thermalprotection to the outer electrode. In some cases, a sleeve is consumableand/or replaceable. For example, if the sleeve contains a targetmaterial that is consumed, the sleeve may eventually be replaced. Inother cases, a sleeve acts as a sacrificial layer that protects theouter electrode from hydrogen embrittlement. In situations where thesleeve itself fails due to hydrogen embrittlement, it may be replaced ata much lower cost than the entire outer electrode.

In some embodiments, the outer electrode may have a porous or mesh-likestructure that allows high energy charged particles to pass through theelectrode while still confining rotating neutrals within the annularspace. Charged particles that pass through the outer electrode may beguided by magnetic fields of an exterior magnet. In some cases, escapingalpha particles are redirected towards hardware (discussed elsewhereherein) capable of converting the kinetic energy of alpha particles intoelectrical energy. In some cases, the pore size in and our electrode maybe less than about 100 microns, in some cases, and in some cases, lessthan about 1 micron. In general, the construction of the inner electrodemay be similar to that of the outer electrode. As with the outerelectrode, the inner electrode may be made of a single material, or itmay have a layered or segmented structure being made of two or morematerials. In some embodiments, the inner electrode may be a solid body,and in other embodiments, the inner electrode has an interior space. Insome cases, the inner electrode may include one or more pathways forinternal cooling. In various embodiments, the inner electrode isconnected to a power supply that provides a current that passes from theinner electrode out to a grounded outer electrode. Materials for theouter electrode are generally also suitable for the inner electrode,although, in certain embodiments, an inner electrode does not includetarget materials or electron emitting materials.

First Embodiment—Magnets

FIGS. 10a-d depict a first embodiment in which an axial magnetic fieldis applied by an electromagnet such as a superconducting magnet. FIG.10a shows an isometric view of a superconducting magnet that surroundsthe outer electrode of the reactor. As depicted, the magnet includes anenclosure 1056. FIG. 10b provides the same perspective as FIG. 10a ,with the enclosure 1056 of the superconducting magnet removed revealingthe superconductive coil windings 1054. FIG. 10c provides a perspectiveof the reactor as viewed along the z-axis and FIG. 10d is an isometricsection view corresponding to the section lines, A-A, shown in FIG. 10c. As shown, the reactor has outer electrode 1010, inner electrode 1020,and a gap 10 that defines the annular space 1040 between the twoelectrodes. An electrical current (as depicted by arrows in FIG. 10a )passes through superconductive coil windings 1054 that wrap around thereactor, creating an applied magnetic field that is substantially in thez-direction through the annular space. In some embodiment, asuperconducting magnet is used to generate an applied magnetic fieldthat passes through the annular space that is between about 1-20 Tesla.In some cases, the applied magnetic field is between 1-5 Tesla. Coilwindings are placed in an insulated enclosure 1056 positioned around thereactor that is kept at low-temperature (e.g., less than −180° C.) andlow-pressure. The enclosure 1056 may be cooled by, for example,adiabatic expansion of gas (e.g., He), or a cryogenic liquid such thatthe temperature of the superconductive coil is kept below its criticaltemperature. In some cases, the enclosure may be cooled mechanically,avoiding any need for liquid cryogens. The coil windings may be madefrom superconducting materials such as niobium-titanium, or niobium-tin,Bismuth strontium calcium copper oxide (BSCC), or Yttrium barium copperoxide (YBCO). Coil windings may take the form of a wire or a tape thatmay be wrapped in an insulating material. In some cases, the coilwindings include any of the aforementioned superconducting materialsplaced in a copper matrix to provide mechanical stability. In someembodiments, commercially sold superconducting magnets may be fromvendors such as Cryomagnetics, Inc., or manufacturers of MagneticResonance Imaging devices. In some cases, a superconducting magnet suchas or similar to the AMS-02 superconducting magnet used for the AlphaMagnetic Spectrometer Experiment may be used. When a superconductingmagnet is used to provide the axial magnetic field, the radius of theconfining wall is typically smaller than the radius of thesuperconducting magnet, for example, in some cases, the radius may belimited to about 20 meters.

When an electromagnet or superconducting magnet is placed around theouter electrode, there may be spacing between the outer electrode 1010and the enclosure of the magnet 1056. This spacing may be used reduceheat transfer to the magnet. In some cases, a heat exchanger may beplaced between the outer electrode 1010 and a magnetic enclosure. Whenthe outer electrode has a porous or mesh-like structure, there may be aspacing between the outer electrode and the enclosure of a magnet thatallows for charged particles that pass through the outer electrode.Charged particles, e.g., alpha particles, passing through the outerelectrode may be constrained in the r-direction by ion cyclotron motionso that they do not collide with the enclosure 1056. In some cases, thespacing between the outer electrodes is between about 3 cm to about 6cm, and in some cases, between about 6 cm and about 10 cm. Chargedparticles may then travel in the z-direction towards energy conversionmeans for generating electrical energy as described elsewhere herein.FIGS. 11a-b depict a reactor in which permanent disk-shaped magnets 1150are placed on either end of the annular space 1140 to generate anapplied magnetic field that is substantially axially directed, i.e., itpoints in the z-direction. FIG. 11a provides a perspective viewed alongthe z-direction, while FIG. 11b provides an isometric section view thatcorresponds to the indicated section lines in FIG. 11a . As depicted inFIG. 11b , the reactor has an inner electrode 1120, an outer electrode1110 forming the confinement wall 1112, and an annular space between theinner and outer electrodes. Magnets 1150 are placed on either side ofthe annular space and have the same magnetic orientation. For example,both magnets may have a north pole facing in the positive z-direction,or both magnets may have a north pole facing in the negativez-direction. While not depicted, in some embodiments the magnets 1150may be ring-shaped such that the magnet is in proximity to the annularspace 1140 and provides a substantially uniform magnetic region alongthe inner surface of the outer electrode 1112. The ring-shaped magnetshave the same pole orientation as the disk-shaped magnets depicted inFIG. 11.

FIGS. 12a-b depict another embodiment in which a plurality permanentmagnets 1250 having the same polarity in the z-direction (e.g., the sameorientation as the disk-shaped magnets depicted in FIG. 11), are placedon either side of the annular space 1240 to generate an applied magneticfield in the z-direction along the inner surface of the outer electrode1212. FIG. 12a provides a perspective in the z-direction, while FIG. 12bprovides an isometric section view that corresponds to the indicatedsection lines, A-A, in FIG. 12a . Some features are labeled in anenlarged view 1201, which depicts how the annular space is bound by theinner electrode 1220, the outer electrode 1210, and permanent magnets1250. Using a plurality of smaller magnets may be useful to reduce costsand physical constraints associated with larger monolithic magnets forlarge-scale reactors. The arrangement of magnets 1250 shown in FIGS. 12aand 12b may be viewed as effectively creating two facing ring magnets.While not shown, in some embodiments a combination of different magnetshapes is used to generate the axial magnetic field. For example, a ringmagnet may be used on one side of the annular space while a plurality ofbar magnets may be used on the other.

FIGS. 13a-c depict an embodiment in which a reactor 1300 with a singleinner electrode 1320 has multiple annular spaces 1340 separated bypermanent magnets 1350 that are arrayed along the z-direction. Asdepicted, the reactor has inner electrode 1320, a plurality of outerelectrodes 1310 that form the confinement wall 1312, which is acombination of wall segments, and an annular space 1340 between eachouter electrode and the inner electrode. FIG. 13a provides a perspectiveviewed along the z-direction, while FIGS. 13b and 13c provide a sectionview and an isometric section view, respectively, that correspond to theindicated section lines in FIG. 13a . When permanent magnets are placedon either end of the annular space, the length of the annular space inthe z-direction may be limited by the strength of the magnetic fieldthat can be generated by permanent magnets. In some cases, the annularspace may be limited to, for example, about 5 or 10 cm. By arrayingmagnets 1350 in the z-direction between a plurality of annular spaces1340, the total surface area on the confinement wall 1312 of the outerelectrode 1310 may be increased. As with previous embodiments, eachmagnet 1350 has the same orientation along the z-axis. This designefficiently uses the permanent magnets between the annular spaces, aseach magnetic pole contributes to shaping the magnetic field that isapplied to a bordering annular space. While the depicted embodiment isshown using ring-shaped magnets, many other shapes may be used; forexample, each magnet bordering an annular space may be made of manysmaller magnets that collectively form a ring-like structure (see FIGS.12a-b ). In some embodiments, the outer electrode 1310 may be segmentedinto physically distinct parts that are electrically isolated. In someembodiments, the outer electrode may be monolithic or otherwiseelectrically connected, for example, such that each outer electrodesegment corresponding to each annular space 1340 is grounded.

FIGS. 14a-c depict an embodiment in which a single reactor structure1400 has multiple annular spaces 1440 separated by permanent magnets1450 that are arrayed along the z-direction. As depicted, the reactorhas a plurality of inner electrodes 1420 and a plurality of outerelectrodes 1410 forming the confinement wall 1412 for the annular space1440 between each set of electrodes. FIG. 14a provides a perspective inthe z-direction, while FIGS. 14b and 14c provide a section view and anisometric section view that correspond to the indicated section lines inFIG. 14a . Rather than employing ring-shaped magnets and a single innerelectrode, as depicted in the embodiments of FIGS. 13a-c , theembodiments of FIGS. 14a-c employ disc-shaped magnets and multiple innerelectrode segments. The description of corresponding features from FIGS.13a-c pertains to the embodiment of FIG. 14a-c . In some embodiments, areactor as shown may operate using only a subset of the availableannular spaces depending on energy demands. For example, in someembodiments fusion reactants are only introduced into one annular spaceand a voltage potential is only applied to the inner electrode adjacentto that annular space. In this manner, the energy output of a reactormay be controlled to meet energy demands, even in real time ifnecessary. Therefore, in some embodiments, individual inner electrodes1420 and/or outer electrodes 1410 are independently controllable.

FIGS. 15a-15c illustrate the magnetic field generated by a series ofring that magnets 1550 are that substantially coaxial and have the sameorientation. FIG. 15a is an isometric view of three magnets, FIG. 15bdepicts a view along the magnet's shared axis, and FIG. 15c is a sectionview corresponding to the line A-A in FIG. 15b . While previousembodiments have made use of magnets that are offset from the annularspace in the z-direction, magnets may also be offset from the annularspace radially in r-direction. As illustrated by the dashed lines inFIG. 15c , each ring magnet, when considered individually, generates amagnetic field 1545 originating at its north pole and ending at itssouth pole. When multiple ring magnets are placed next to each other,the net effect can be a combined magnetic field that is a superpositionof the individual magnet fields and substantially pointed along theshared axis as indicated by the solid magnetic field lines 1546. Thismagnet configuration may be used to extend the feasible length of anannular space of a reactor while using permanent magnets.

FIGS. 16a-16c illustrate an embodiment using radially offset ringmagnets 1650 to generate an axial magnetic field through the annularspace. As depicted, the reactor has a single inner electrode 1620 and asingle outer electrode 1610 that forms the confinement wall 1612 for theannular space 1640 between the electrodes. FIG. 16a provides aperspective of the reactor as viewed along the z-direction, while FIGS.16b and 16c provide a section view and an isometric section view thatcorrespond to the indicated section line in FIG. 16a . Each of themagnets 1650 has the same polarity along the z-direction. For example,as depicted, each of the magnets 1650 has its south pole facing in thepositive z-direction. This embodiment allows for an extended annularspace in the z-direction, creating a larger surface area on theconfining wall 1610 and allowing for a greater power output potential.Overlapping features from corresponding embodiments of FIGS. 13 and 14may apply to the embodiments of FIGS. 16a -c.

FIGS. 17a-17c illustrate an embodiment using radially offset magnets(1750, 1752) to generate an axial magnetic field through a singleannular space. As depicted, the reactor has a single inner electrode1720 and a single outer electrode 1710 that forms the confinement wall1712 for the single annular space 1740 between the electrodes. FIG. 17aprovides a perspective of the reactor as viewed in the z-direction,while FIGS. 17b and 17c provide a section view and an isometric sectionview that correspond to the indicated section line in FIG. 17 a. Theembodiment of FIGS. 17a-c goes beyond the embodiment described withrelation to FIGS. 16a-c in that additional magnets 1752 are placed inthe interior region of the inner electrode 1620. As depicted, theadditional magnets 1752 have the same orientation along the z-directionas the exterior magnets 1750. In some embodiments, as depicted in FIGS.17b and 17c , the inner ring magnets 1752 are aligned with the outerring magnets 1750 in the z-direction. In some embodiments, the innerring magnets may be offset from the outer ring magnets, or the spacingbetween magnets may differ from the spacing of the outer magnets. Insome embodiments, the interior magnets may take a different shape thanthe exterior magnets, e.g. the interior magnets may be bar magnets.

In some embodiments, permanent magnets are made from rare earth elementsor alloys of rare earth elements. Examples of suitable magnets includesamarium-cobalt magnets and neodymium magnets. Other strong magnetsknown now or later developed may be suitable for use. In someembodiments permanent magnets may be used to generate a field that thatis between about 0.1 and 1.5 about Tesla in the annular space; in someembodiments, permanent magnets may generate a magnetic field betweenabout 0.1 and about 0.5 Tesla in the annular space.

Not all reactors require permanent magnets. Some employ electromagnetsor superconducting magnets as explained with reference to FIGS. 10a-d .Some reactors employ a combination of two or more of a permanent magnetand an electromagnet. FIGS. 18a-d depict a first embodiment in which anaxial magnetic field is applied by an electromagnet. As depicted, thereactor has an inner electrode 1820 and an outer electrode 1810 thatforms the confinement wall 1812 for the annular space 1840 between theelectrodes. FIG. 18a shows an isometric view of an electromagnet that isplaced over the reactor. FIG. 18b provides a perspective of the reactoras along the z-axis and FIGS. 18c and 18d depict a section view and anisometric section view corresponding to the section lines shown in FIG.18b . An electrical current is passed through coil windings 1854 thatwrap around reactor in the z-direction to create an applied magneticfield that is substantially in the z-direction through the reactor asdepicted by the magnetic field lines in FIG. 18c . The electricalcurrent through the electroconductive coil may be provided by an AC or aDC power supply. In cases where the electroconductive coil is driven byan AC power supply, the inner electrode and/or outer electrode may alsobe driven by an AC power supply at the same frequency. This is done suchthat the rotation of charged particles is maintained in the samedirection, rather than in alternating directions as would occur if thealternating polarity of the magnetic field was not synchronized with theelectric field. The coil may be made from a conductive material such ascopper, aluminum, gold, or silver. In some embodiments, the coil takesthe form of a wire that is wrapped around the outer electrode, in someembodiments the coil is placed in a separate enclosure that may beplaced around the outer electrode.

Reverse Electrical Polarity Embodiment

A reverse electrical polarity rotor was previously described in FIGS. 5ato 5c . Generally, unless stated otherwise, the structure of electrodescorresponding to the first embodiment are also descriptive of a reverseelectrical polarity rotor. For example, materials for inner and outerelectrodes, the gap between electrodes (542 in FIG. 5a ), and theconfigurations of magnets used to produce a magnetic field in thez-direction may be the same as described for the concentric electrodereactors. However, as explained below, some embodiments employ differentstructural configurations and/or different materials (e.g., differentmaterials on the inner electrode).

FIG. 5d depicts a cross selection of a reverse electrical polarityrotor. An electric field may be applied in the negative r-direction byapplying a negative voltage to the inner electrode and grounding theouter electrode, by grounding the inner electrode and applying apositive potential to the outer electrode, or by applying a morenegative potential to the inner electrode than is applied to the outerelectrode. When an electric field is generated by applying an electricpotential to the inner and/or outer electrode, positively chargedparticles in the annular space 540 are drawn towards the inner electrode520. As the charged particles move inward, a Lorentz force azimuthallyaccelerates the particles which may result in a spiraled trajectory asillustrated by path 503. Through ion-neutral coupling, neutrals in theannular space are co-rotated along with the positively chargedparticles. Due to the potential difference between the inner and outerelectrodes, a surplus of electrons on the inner electrode forms anelectron-rich region 532 proximate to the electrode surface that rotatesin the same direction as the positively charged particles due to theLorenz force. As discussed elsewhere, this electron-rich region mayreduce the Coulombic barrier between fusing nuclei. In some cases, thiselectron-rich region may extend out about 100 um to about 3 mm from thesurface of the inner electrode.

In some cases, when positively charged particles move inward,recombination of charged species occurs when a positively chargedparticle contacts the inner electrode or when a positively chargedparticle encounters a free electron in the electron-rich region. In somecases, a positively charged particle may orbit the inner electrode at aLarmor radius 502. In some embodiments, the concentration of positivelycharged particles may vary in the radial direction. For example, theremay be a higher concentration of positively charged particles circlingthe annular space at a Larmor radius, than near the outer electrode.This gradient of charged particles may result in a velocity distributionwithin the annular space with particles tending to move more slowly nearthe outer wall where there is a higher concentration of neutrals due toa centrifugal force and fewer positively charged particles to drive theneutrals into motion.

In some configurations, an inner electrode is constructed from a singlematerial such as tantalum, tungsten, copper, carbon, or lanthanumhexaboride. In some cases, an inner electrode has a conductive core 520a that is coated with an electron emitting and/or target material 520 b.For example, the inner electrode may have a core made from a conductiveand heat resistant material, e.g., tungsten, which is coated withlanthanum hexaboride, boron nitride, or another boron-containingmaterial. In some cases, the inner electrode has a diameter that isbetween about 1 cm and about 3 cm, and in some cases, between about 4 cmand about 6 cm. In some cases, the inner electrode has a tinycross-section, for example, it may be a filament or wire. In suchembodiments, the inner electrode may have a diameter less than about 0.5mm, less than about 0.1 mm, or less than about 0.05 mm. In some cases,the inner electrode may extend between about 3 cm and about 10 cm inlength in the z-direction. In some cases, the inner electrode may besmall in the z- direction, e.g., less than about 3 cm, or less thanabout 1 cm. In some embodiments, the inner electrode may be much longerin the z-direction, e.g., longer than about 20 cm. In some cases, theconfinement region in the z-direction for a reverse electrical polarityreactor (the length that the inner and outer electrodes overlap) may belimited by the power source that applies a charge to the inner and/orouter electrode. In some cases, the length in z-direction may depend onthe gas pressure within the confinement region. In some cases, the powerneeded to generate a plasma within the annular space may be reduced ifthe gas pressure is reduced to a very low pressure allowing for anincreased length in the z-direction.

FIG. 19a depicts several methods by which the inner electrode may beactively cooled. In some cases, inner electrode 1910 has an internalpathway 1928 through which a passing fluid removes heat. For example,water may be pumped through the internal pathways to remove heat fromthe inner electrode. In some cases, an inner electrode may be joined toa ceramic block 1923 that is thermally conductive and electricallyinsulating. A ceramic block may be made of materials such as aluminumoxide. Heat is dissipated through the ceramic block, removing heat fromthe end of the inner electrode to which it is connected. In some cases,a ceramic block contains an opening or hole to support the innerelectrode. In some cases, an inner electrode is fixed to the ceramicusing a set screw. In some cases, the heat conducted through the ceramicblock is used to generate electrical power, e.g., via thermoelectricgenerators or heat exchangers that are coupled to the ceramic block.

In some cases, the inner electrode may be replaced if the targetmaterial is consumed or if the electrode is damaged. For example, aboron coated filament that is used as an inner electrode may be replacedwhen the boron coating is consumed or when the filament breaks.

In certain embodiments, the length of the inner electrode extends beyondthe annular space (as defined by the z-direction edges of the outerelectrode). In some cases, the position of the inner electrode isadjusted in the z-direction, e.g., via a linear actuator. For example,if the inner electrode is a wire, the wire may be drawn through theannular space during operation of the reactor to prevent the innerelectrode from melting, or to replace a section of the wire where atarget material (e.g., a boron coating) has been consumed.

In some cases, the width of the inner electrode may vary in thez-direction. FIG. 19b depicts a configuration in which the innerelectrode 1920 extends beyond the outer electrode 1910 and is held inplace by a sleeve 1921 that may act as an extension of the innerelectrode. Sleeve 1921 may be made from conductive materials such ascopper, stainless steel, and tantalum. In some cases, a potential may beapplied to the inner electrode through the sleeve; this may reduceresistive heating to inner electrodes that have a small diameter. Insome cases, the diameter of the sleeve may be much greater than that ofthe inner electrode. For example, the diameter of the sleeve may begreater than about 10 cm while the diameter of the inner electrode isless than about 0.5 mm. In some configurations, the inner electrode maybe fixed to the sleeve using set screws. In some embodiments, the sleevemay be threaded directly into the sleeve. These and other attachmentmechanisms may allow the inner electrode 1920 to be replaceable, whilethe sleeve 1921 is permanent. In some cases, the sleeve may be coatedwith a target material such as boron. In some cases, a sleeve may beinternally cooled as discussed in FIG. 19 a.

As with the reactors of the first embodiment, the gap between the innerand outer electrode may be limited by a power supply's ability togenerate a plasma in the confinement region. In some cases, the outerelectrode may be similar in construction to the outer electrodedescribed for the first embodiment. In some cases, the outer electrodemay have an exterior insulating layer. This may be useful, e.g., if analternating signal is applied the electrodes of a reactor, or if thereverse electrical polarity reactor is part of a modular unit consistingof additional reactors that need to be electrically isolated from oneanother. In general, the supporting structure of both the inner andouter electrode may include electrically insulating materials insulatethe electrodes from the housing of the reactor, and prevent alternativecurrent paths between the electrodes. In some cases, the outer electrodeis a metallic sheet (e.g., a copper sheet) that is confined to acylindrical shape by being placed within a quartz tube. In some cases,an outer electrode is a solid tubular structure that is placed within aninsulating structure. In another embodiment, the electrode is made bycoating the interior surface of a quartz tube with a metallic conductivecoating.

As discussed elsewhere, only a small number of ions or positivelycharged particles are needed to drive many neutral particles intorotation. Due to the confining wall associated with the outer electrode,the concentration of neutrals increases in the radial direction.Rotating neutrals, however, are unaffected by the radial electric fieldor the axial magnetic field. Due to randomized collisions with the outerwall and other particles, neutrals may be deflected into theelectron-rich region, and in some cases, neutrals may impact a targetmaterial on the inner electrode resulting in fusion events. Likewise, insome cases, positively charged particles may also be deflected into theinner electrode producing a fusion reaction, e.g., a proton-boron¹¹fusion reaction.

In some cases, a reverse electrical polarity reactor is operated at aconstant voltage. For example, a voltage supply may apply a potential tothe inner electrode and/or outer electrode so that a constant orsubstantially constant potential difference between the electrodes ismaintained during operation of the reactor. In another mode ofoperation, a reverse electrical polarity reactor is operated at aconstant current. Operating at constant current may be beneficial whenthe inner electrode is small and susceptible to failure due to resistiveheating. In some cases, a reactor is initially operated using constantvoltage and then transitioned to a constant current mode of operation.

In some configurations, an energy storage device such as a capacitor ora battery is used to apply a potential to the inner electrode and/orouter electrode to initiate a fusion reaction. In some cases, circuitryregulates the current and/or voltage supplied by the energy storagedevice. In some cases, an energy device (e.g., a capacitor) is connectedto the inner electrode and/or outer electrode and discharged until theenergy storage device is no longer capable generating an electric fieldstrong enough to support a fusion reaction. In some cases, a reactor isconfigured with an additional energy storage device that is charged byelectrical energy generated from the fusion reaction while the firstenergy storage device is discharged. A controller may then operate aswitch that that alternates the energy storage devices between chargingand discharging modes, so that a fusion reaction may be maintained.

In some cases, a power supply is disconnected from either the innerand/or outer electrode, and a fusion reaction may continue to occur fora period (e.g., about 10 seconds) before the potential differencebetween the electrodes is no longer sufficient to sustain the fusionreaction. When the electric field becomes too small to sustain fusion,the voltage or current source may again be reconnected to apply anegative potential to the inner electrode.

Before the operation of a reverse polarity reactor, the gas in theannular space may be at be at a pressure of about 1 atm or higher. Insome cases, such as when the inner electrode is long in the z-direction,an inner electrode may have a low pressure to reduce the power needed toinitiate a fusion reaction. In some cases, the pressure within theannular space may be reduced to less than about 1 Torr or less thanabout 10 mTorr before operating the reactor. In some cases, the pressurewithin the annular space may be adjusted through inlet and outlet valvesto control the rate of a fusion reaction.

For a reverse electrical polarity reactor, the magnetic field in theconfinement region is sometimes greater than about 0.5 Tesla, andsometimes greater than about 1 Tesla, and sometimes greater than about 3Tesla. In some embodiments of a reverse electrical polarity reactor, themagnetic field is not substantially perpendicular to the electric fieldbetween the inner and outer electrodes. In some embodiments, themagnetic field is not uniform through the confinement region. Themagnetic field in the confinement region may be tuned by adjusting theplacement and orientation of magnets and/or electrodes. In some cases, anon-uniform magnetic field may increase the rate at which ions andneutrals collide with the inner electrode. In general, the appliedmagnetic field and/or the potential applied to electrodes may varydepending on the geometry of a reactor, the reactant gas composition,and the reactant gas pressure.

During operation, the concentration of particles, particularly highermass particles, is greater near the outer wall due to the centrifugalforce. This may be helpful in extracting fusion products, which have ahigher mass than the rotating reactants, from the annular space. Forexample, when alpha particles are produced by a fusion reactioninvolving a rotating hydrogen species, alpha particles may beconcentrated near the outer wall where they may then be removed throughan outlet valve. In some cases, fusion products may be pumped intoanother reactor in which the fusion products are used as reactants. Forexample, alpha particles or helium atoms produced in a reverseelectrical polarity reactor may be moved to another reactor configuredto support a helium-helium fusion reaction.

Reverse Fields Reactor Embodiments

Another reactor embodiment has a reverse fields configuration wasdescribed previously with relation to FIGS. 6a-d . This configurationemploys a Lorentzian rotor to impart and maintain rotational movement ofparticles in an annular space. Generally, many of the reactors describedherein may be reconfigured to apply reverse fields, albeit with theorientation of the magnetic field and electric field transposed.

A magnetic field in the radial direction may be applied using permanentmagnets (616, and 626) made from a magnetic material such as thosedescribed in relation to the first embodiment. In some cases, permanentmagnets may be replaced with a plurality of azimuthally offsetelectromagnets having radially orientated axes, such that a magneticfield, oriented substantially in the r-direction, is applied throughoutthe annular space. In some cases, the surface of the confining wall mayinclude one or more layers that protect a magnetic material. Forexample, a layer of aluminum or tantalum may provide protection toeither an exterior or interior magnet. In some cases, a protective layermay include a target material containing a fusion reactant or anelectron emitter. In some cases, a confining wall may have an internalcooling system to keep material below its melting temperature andprevent magnets from demagnetizing.

In concentric electrode embodiments, the gap between the inner electrodeand the outer electrode is sometimes constrained by the available powerto ionize gas in the annular space. Similarly, in a reverse fieldsconfiguration the confinement region in the z-direction that separateselectrodes 660 a and 660 b may be constrained. For example, in somecases, the spacing between electrodes is in the range of about 1 mm toabout 50 cm, and in some cases, the spacing is between electrodes is inthe range of about 5 cm to about 20 cm.

In concentric electrode embodiments, the length of the annular space inthe z-direction may sometimes be limited by the strength of permanentmagnets. Similarly, in a reverse fields configuration, the gap in ther-direction may sometimes be limited by the need to create a strongmagnetic field near the surface of the confinement wall. In some cases,the radial gap may be limited to, for example, about 10 cm or less, orabout 5 cm or less. In some cases, as when magnet 616 providessufficiently strong magnetic field near the confinement surface byitself, the gap may be larger; for example, in some cases, the gap maybe larger than about 10 cm. In some cases, the interior magnet may notbe necessary.

Wave-Particle Reactor Embodiments

An alternative reactor configuration, sometimes referred to as thewave-particle embodiment, was briefly described previously and isdepicted in FIGS. 7a and 7b . In a wave-particle embodiment, chargedparticles are driven into rotation by oscillating electrostatic fields.The neutral species are pushed along by the charged particles. Electricfields are created by applying charge to azimuthally separatedelectrodes located on the confinement wall, an interior wall, or anotherstructure in communication with the confinement region. Since thisembodiment does not require a magnetic field, the structural limitationsimposed by using magnets do not apply. For example, the radius of thereactor may be larger than what is feasible for ring or disk-shapedmagnets. Further, because the embodiment does not require current flowbetween an inner and an outer electrode, structural limitations imposedby concentric electrodes do not apply. In some embodiments of awave-particle design, the radius of a confinement wall may be greaterthan about 2 meters, in some cases greater than about 10 meters, and insome cases greater than about 50 meters. In contrast to someimplementations of a Lorentzian rotor, the length of a reactor in thez-direction is not limited by the strength of permanent magnets as maysometimes be the case in concentric electrode embodiments. In someembodiments, a confinement region (e.g., an annular region) may have alength in the z-direction that is greater than about 1 meter, in somecases, greater than about 10 meters, and in some cases greater thanabout 100 meters. In one embodiment there is a curvature in thez-direction of a reactor so that that the confinement wall forms a torusor torus-like shape. In general, the size limitations of a reactor maybe governed energy demands of the reactor and costs associated withproduction. In a wave-particle embodiment, a degree of control over therotating species may be set by defining the number and size of theazimuthally offset electrodes impacting the confinement region. Arelatively greater number of electrodes along the confinement wallallows the electric field lines to be more finely modulated, which canimprove the efficiency at which the electric field is used to movecharged particles. In some cases, this is because the dynamicallychanging electric field drives particles points primarily in theazimuthal direction rather than the radial direction. Generally, areactor will have at least three azimuthally separated electrodes. Somereactors may have at least five azimuthally spaced electrodes, somereactors may have more than about 50 azimuthally spaced electrodes. Insome designs, the number of electrodes scales with a size of a reactor.For example, a reactor having a radius of about 1 meter may have betweenabout 20 and about 40 azimuthally spaced electrodes along theconfinement wall while a reactor having a radius of about 2 meters mayhave about 40 to about 80 azimuthally spaced electrodes. In some cases,the ratio of a reactor's circumference, in meters, to the number ofazimuthally spaced inner or outer electrodes is between about 3 andabout 150, and in some cases, the ratio is between about 20 and 100.

In some cases, the electrodes are separated by an electricallyinsulating material such as aluminum nitride or boron nitride. Theinsulating material may be sufficiently thick so that the material doesnot experience electrical breakdown. The minimum thickness may bedetermined by the dielectric strength of the insulating material and thevoltage applied to electrodes. In some cases, an electrically insulatingmaterial contains a target material (fusion reactant such as boron-11)and/or an electron emitter.

In some cases, the width of an electrode in the azimuthal direction isless than about 10 cm, in some cases less than about 5 cm, and in somecases less than about 2 cm. The electrodes may have any of variousshapes. For example, they may be circular or polygonal. In some cases,they are rectangular. In some embodiments, a reactor utilizesazimuthally separated electrodes only along the confinement wall.Alternatively, in some embodiments, a reactor utilizes electrodes onlyalong an inner wall, or only electrodes that bound the confinementregion in the z-direction (e.g., electrode placement may correspond toelectrodes 660 a and 660 b of the reverse fields embodiment depicted inFIG. 6c ). In cases where electrodes do not themselves define theconfinement wall, the surface of the confinement wall may be made ofanother material such as a target material or an electron emitter. Forexample, the electrodes may be separated from the confinement region bya sleeve that contains coupons made from lanthanum hexaboride.

In some cases, the confinement-wall wall is configured with a thermalmanagement component such as a heat exchanger (e.g., a cooling jacket).A heat exchanger can be used to prevent electrodes from overheatingand/or supply to provide heated fluid to a heat engine for generatingelectrical or heat energy. In some cases, heat may be dissipated from areactor by passing a fluid such as water through passageways in theconfinement wall. For example, insulating material separatingazimuthally separated electrodes may have internal passages throughwhich fluid is passed.

In concentric electrode embodiments, the gap between an inner electrodeand outer electrode is sometimes constrained due to the limited poweravailable to ionize gas in the confinement region. In a wave-particleconfiguration, the gap between adjacently located electrically isolatedelectrodes may also be constrained. For example, in some cases, thespacing between electrodes is, on average, in the range of about 1 mm toabout 50 cm, and in some case, the spacing is between electrodes is, onaverage, in the range of about 5 cm to about 20 cm.

In some cases, a wave-particle reactor has more than one mode ofoperation. For example, a first phase may be employed to initiate orstrike a plasma and a later phase may be used drive ions (and indirectlyneutrals) in a rotational direction. For example, an RF electric fieldmay be applied radially between the inner electrodes and the outerelectrodes to generate a weakly-ionized plasma to prepare a reactor foroperation. Once the plasma has been generated between the inner andouter electrodes, the reactor may transition to a mode where drivesignals are sequentially applied to the azimuthally distributedelectrodes to drive charged particles and neutrals into rotation.

Oscillating signals applied to azimuthally distributed electrodes todrive rotation of ions and neutrals may be provided over a wide range offrequencies chosen based on the reactor configuration and the desiredrotational velocity. For example, the drive signals may be applied at afrequency in the range of about 60 kHz to 1 THz, and in some cases inthe range of about 60 kHz and 1 GHz. In some cases, the frequency of adrive signal may begin low and then increase, gradually or abruptly. Forexample, the drive signal may start at a relatively low frequency, e.g.60 kHz and eventually ramp up to a much higher frequency, e.g., 100 Mhz.

In some cases, a drive signal applies charge using a controlled voltage.To avoid arcing between electrodes electrodes, charge is ideally applieda high voltage and low current, rather than high current at low voltage.In some cases, a drive signal applies between about 1 kV and about 100kV to azimuthally separated electrodes. In some cases, a drive signalmay apply more than 100 kV to electrodes.

Using electrostatic forces, a wave-particle embodiment may inducerotational velocities that exceed that typically found in Lorentziandriven reactor having a similar reactor configuration (e.g., a similarconfinement radius). In some cases, an electrostatically driven reactormay drive rotation of a gaseous species at a rate of at least about 1000RPS, or in some cases at least about 100,000 RPS. In a wave-particleembodiment, a control system may be used to direct how charges areapplied to the electrodes. In some cases, a control system uses adetected velocity, determined using a high-speed camera or anothersensor, as feedback to adjust a charge sequence that is applied to theelectrodes. In general, azimuthally separated electrodes may havesimilar structural considerations and may be made from similar materialsto those described in relation to the above embodiments that employmagnetic fields.

Hybrid Reactor Embodiments

Another general reactor configuration, which may be referred to as ahybrid reactor configuration, was briefly described with relation toFIGS. 6a to 6f . This configuration employs both a Lorentzian rotor anda wave-particle driver to impart and maintain rotational movement ofparticles in an annular space. When operating a Lorentzian rotor in ahybrid reactor, some aspects of the above-description of the reversefields embodiment may apply. Similarly, when operating using azimuthallyspaced electrodes of the hybrid reactor, some aspects of theabove-description of the wave-particle embodiment may apply.

As in the reverse fields embodiments, a magnetic field in the radialdirection may be applied using permanent magnets (616, and 626) whichmay be made from magnetic materials such as those described in relationto the first embodiment. In some cases, permanent magnets may bereplaced with a plurality of azimuthally offset electromagnets havingradially orientated axes, such that a magnetic field, orientedsubstantially in the r-direction, is applied throughout the confinementregion. In some cases, the surface of the confining wall may include oneor more layers that protect a magnetic material. For example, a layer ofaluminum or tantalum may provide protection to either an exterior orinterior magnet. In some cases, a protective layer may include a targetmaterial containing a fusion reactant or an electron emitter. In somecases, a confining wall may have an internal cooling system to keepmaterial below its melting temperature and prevent magnets fromdemagnetizing.

In concentric electrode embodiments, the gap between the inner electrodeand the outer electrode is sometimes constrained by the available powerto ionize gas in the annular space. Similarly, in a hybrid reactorconfiguration the confinement region or annular space in the z-directionthat separates electrodes 660 a and 660 b may be constrained. Forexample, in some cases, the spacing between electrodes is in the rangeof about 1 mm to about 50 cm, and in some cases, the spacing is betweenelectrodes is in the range of about 5 cm to about 20 cm.

In concentric electrode embodiments, the length of the annular space inthe z-direction may sometimes be limited by the strength of permanentmagnets. Similarly, in a hybrid configuration, the gap in ther-direction may sometimes be limited by the need to create a strongmagnetic field near the surface of the confinement wall. In some cases,the radial gap may be limited to, for example, about 10 cm or less, orabout 5 cm or less. In some cases, as when magnet 616 providessufficiently strong magnetic field near the confinement surface byitself, the gap may be larger; for example, in some cases, the gap maybe larger than about 10 cm. In some cases, the interior magnet may notbe necessary.

In a hybrid embodiment, a control system may be used to direct howcontrol signals are applied to the azimuthally separated electrodes. Insome cases, a control system may receive feedback from sensors to adjusta charge sequence that is applied to the electrodes. In general,electrodes (660 a and 660 b) may have similar structural considerationsand may be made from materials described as being suitable forelectrodes in the first embodiment.

In some configurations, a hybrid reactor is configured to transitionbetween operating modes while conducting a fusion reaction or just priorto conducting a fusion reaction. For example, the reactor may operateinitially using a Lorentzian rotor before transitioning to awave-particle driver to maintain particle rotation. Under certainconditions, a Lorentzian driven rotor may be more efficient atinitiating rotation of particles in the annular space. Once particleswithin the annular space have reached a critical state of rotationwithin the reactor in which the benefit of using a Lorentzian rotor isno longer seen, the reactor may switch to a wave-particle drive mode ofoperation. In some cases, by transitioning to a wave-particle drivingmode of operation, greater particle velocities and thus greater energyproduction may be achieved. In some cases, by transitioning to awave-particle driving mode of operation, energy production may bemodulated with greater precision by adjusting the sequence of drivesignals that are applied to the azimuthally distributed electrodes (660a and 660 b). In some embodiments that use electromagnets to generate anelectric field, a current supply used to control the magnetic field maybe terminated when the reactor enters a wave-particle mode of operation.This may be useful to prevent a Lorentzian force from acting on chargedparticles in the z-direction.

Electron Emitters

As described elsewhere herein, a confining wall is sometimes made atleast in part of an electron emitting material, referred to herein as anelectron emitter. These materials may emit electrons via thermionicemission above a certain temperature. For example, some boron basedelectron emitters have an emission temperature that is in the range ofabout 1500 K to about 2500 K. In some cases, an electron emitter may bein the form of a powder that is compacted, sintered, or otherwiseconverted to a form suitable for placement within the annular space. Insome cases, an electron emitting material may be sintered or depositedusing physical vapor deposition onto the confining wall of a reactor. Inother cases, an electron emitter may be forged into a continuousstructure that forms part of the confining wall or is attached to theconfining wall.

Some electron emitters are materials having a low work function that donot degrade when exposed to the thermal and other conditions within areactor. Examples of electron emitters include oxides and borides suchas barium oxide, strontium oxide, calcium oxide, aluminum, oxide,thorium oxide, lanthanum hexaboride, cerium hexaboride, calciumhexaboride, strontium hexaboride, barium hexaboride, yttrium hexaboride,gadolinium hexaboride, samarium hexaboride, and thorium hexaboride. Insome cases, emitters may be carbides and borides of transition metals,e.g. zirconium carbide, hafnium carbide, tantalum carbide, and hafniumdiboride. In some cases, emitters may serve as a reactant of a fusionreaction such as ⁶Li, ¹⁵N, ³He, and D. In some cases, an electronemitter may be a compound that includes a fusion reactant. For example,lanthanum hexaboride may act as both an electron emitter and a targetmaterial for proton-¹¹B fusion. In some cases, a fusion reaction productmay serve as an electron emitter. In some cases, an electron emitter maybe a composite of two or more materials, where at least one material hasa low work function and emits electrons during operation.

In some cases, an electron emitter is attached as a solid element in theconfinement wall of a reactor. In some embodiments, electron emitters,which may be provided in the form of coupons, have a thin or flatstructure and are attached to the confining wall without protrudingsignificantly into the annular space. FIG. 20a depicts severalillustrative cross-sections of electron emitters. In some embodiments,these electron emitters may be attached to the surface of the confiningwall using a mechanical fastener such as a clip, or a screw. In somecases, an electron emitter is configured to slide into a slot within theconfinement wall and is held in place by, at least partially, friction.For example, a slot may have grooves or a clamping mechanism for holdingan electron emitter in place. In some cases, emitters are attached tothe confining wall by heat, adhesive, or another process. In some cases,the emitter structures have a thickness that is less than about 1.2 cm,in some cases less than about 6 mm, and in some cases less than about 3mm. The dimensions of an electron emitter in the azimuthal direction orthe z-direction may be limited by the physical dimensions of a reactor.FIG. 20b depicts several configurations in which electron emitters 2036may be distributed symmetrically along the surface of the confining wall2010, however in some configurations electron emitters may be positionedin only a few select regions.

In certain embodiments when emitters are disposed on the surface of theconfining wall, they are heated by frictional and/or plasma heat that isintrinsic to the operation of the reactor. In some cases, an additionalmethod may be used to add energy to an electron emitter to increase therate of electron emission. An additional method may be used to heat anemitter during initial operation of a reactor when it is stillrelatively cool. In some cases, additional methods of increasingelectron emission may be used to control the rate of a fusion reaction.

In some embodiments, an electron emitter on the confining wall iselectrically connected to a power supply to enhance electron emission.For example, in some embodiments, a current is passed through a filamentwithin an electron emitting material to provide Joule heating. In somecases, a filament is made of a refractory metal such as tungsten. Insome cases, such as when the confining wall is grounded, the electronemitter may be separated from a grounded portion of the confining wallby an electrically insulating material. In some cases, a direct currentis applied to a filament. In some cases, electron emission is furtherimproved or controlled by applying an alternating current to an electronemitter; for example, a current having an RF or microwave signal.

FIGS. 21a-b depict an example in which Joule heating may be used tocontrol electron emission in a reactor having concentric electrodes.FIG. 21a provides a view in the z-direction of the reactor having aninner electrode 2120, an outer electrode 2110 separated from the innerelectrode by the confinement region (e.g., an annular space) 2140, andelectron emitting modules 2136 placed along the confining wall 2112 thatare powered by a power supply 2135. FIG. 21b provides an enlarged viewof an electron emitting module located on the confining wall. Anelectron emitting module includes an electron emitter material 2130,such as lanthanum hexaboride, that is heated by a filament 2134. In somecases, the module may include insulating layers, depicted as 2137 and2138, which may provide electrical and/or thermal isolation from theouter electrode and/or confining wall (assuming they are different).These insulating layers may be made out of ceramic materials such aszirconium oxide, aluminum oxide, zinc nitride, and magnesium oxide. Insome embodiments, the position of the electron emitting modules may beadjusted during operation of the reactor. For example, to increaseelectron emission caused by frictional heating of the rotating species,a module may be moved radially inward into the confinement region usingan actuator. Alternatively, to limit a reaction, a module may be pulledout of the confinement region in order to limit the electrons beingreleased.

In some embodiments, electron emitters may have a sharp point or a coneshaped structure at one end for improved field electron emission. Forexample, when an electron emitter is supplied with an electricpotential, a strong electric field occurring near the point as a resultof the narrowing geometry may cause field electron emission focused atthe location of the point.

In some embodiments, one or more lasers are used to increase orotherwise control electron emission from an emitter. As depicted in FIG.22, a reactor 2200 may be configured with a laser 2231 to direct lightwithin the confinement region 2240 onto an electron emitter 2230. Asdepicted, light from a laser may be optically directed through or alongan inner electrode 2220 via an insulated optical fiber 2239. Whilelasers may be directed at emitters that are used for thermionicemission, they may also be directed at other materials such as titaniumon the confinement wall that may exhibit the photoelectric effect. Forexample, metals and conductors may exhibit the photoelectric effect whenimpinging photons create a charge imbalance that is not neutralized bycurrent flow. While FIG. 22 depicts a first embodiment, in a reverseelectrical polarity embodiment, a laser may be directed towards theinner, negatively charged electrode, to increase electron emission.

Gas Delivery System

A reactor may have one or more gas valves that for introducing fusionreactants and removing fusion product. In some cases, standardized gasvalves may be used. For example, gas valves used for low-pressuredeposition and etching chambers may be suitable for the reactor. In somecases, a gas reactant is released into the confinement region at alocation interior location; for example, a reactant species may berouted through an inner electrode. In some cases, a gas valve may belocated at one end of the confinement region or annular space in thez-direction, and in other cases a gas reactant species is introducedinto the confinement region through a valve located within the confiningwall. Outlet valves for fusion products may be placed at similarlocations to the inlet valves. When fusion products are removed duringoperation of a reactor, outlet valves may be located on the confinementwall or at a location adjacent to the confinement wall, but offset fromthe confinement region in the z-direction. In some cases, an inlet andoutlet valves may need to be electrically insulated from an electrode soas not to cause an electrical short to ground.

Inlet and outlet valves may also be accompanied with vacuum or pumpsystems to aid in the transport of gas species into and out of areactor. In some cases, valves may include flow meter that controls theamount of gas species added into or removed from a reactor. In somecases, a flowmeter may be connected to a control system of the reactorto carefully limit the amount of hydrogen, or reactant species that isput into the chamber. In some cases, a gas inlet introduces neutralsnear the confinement region and a gas outlet removes neutrals that havemigrated beyond where fusion is occurring in the z-direction of areactor. In some cases, a pumping system that controls the distributionof neutrals along the z-direction of a reactor is used to removeneutrals that might otherwise reduce the efficiency of converting thekinetic energy of fusion products (e.g., alpha particles) intoelectrical energy.

While the embodiments discussed describe gas species, in otherembodiments fusion reactants are introduced into the confinement regionin liquid form. In some cases, rather than filling the confinementregion with a fusion reactant in the form of a gas, the confinementregion may be filled or partially filled with a liquid fuel. Forexample, liquids containing available or easily releasable hydrogen suchas liquid hydrogen, ammonia, alkanes such as butane or methane, andliquid hydrides may be used in place of gaseous hydrogen. In some cases,a liquid fuel is provided in a manner that quickly vaporizes afterentering a chamber. In some cases, adding a liquid fuel to a reactor isused to control the pressure within the reactor. For example, by usingtemperature differentials and the known volume of the confinementregion, the pressure within the confinement region may beback-calculated using the ideal gas law. In some cases, the gas reactantpressure within a reactor may be carefully monitored so that a highneutral density is maintained and yet the structural integrity of thereactor is not compromised.

When a reactor is a Lorentzian rotor, liquid fuel may be added insufficient quantity or under thermal conditions that the liquid does notimmediately evaporate upon entering the confinement region. In suchcases, a current may be passed through the liquid fuel by applying apotential between electrodes. In some cases, a liquid seeded withcharged particles such as potassium. In the presence of a magneticfield, the Lorentzian force drives the charged and neutral components ofthe liquid fuel into rotation. As the kinetic energy of the rotatingcolumn increases, the liquid near the boundary layer along the confiningwall may vaporize, releasing hydrogen gas or another reactant gas thatmay fuse with a target material on the confining wall. For example,proton-¹¹B fusion may occur when hydrogen gas is released from theliquid fuel, and the confining wall contains lanthanum hexaboride. Insome cases, the gaseous layer which develops between the rotating liquidand the confining wall may create a slip layer that allows the liquid inthe confinement region to rotate even faster by decreasing the dragimposed by the liquid-wall interface. In some cases, a liquid may absorbheat and may reduce concerns of melting the electrodes. Since liquidsmay have high densities of the fusion reactant compared to gases, theliquid may be used for extended periods without needing replacement.While not limited to embodiments which use liquid fuel, in some cases areactor may have a safety valve to release gas from a reactor if thepressure exceeds a threshold value. In some cases, such as intransportation applications, a fusion reactant may be stored in liquidform and delivered to a reactor as a liquid or vaporized prior todelivery. By storing fusion reactants in a liquid form, a fuel supplymay be small and compact.

In some cases, a liquid fuel may be supplied to a reactor by apressurized tank. In some cases, a fusion reactant (e.g. hydrogen) maybe may be contained in small capsules that are provided to a reactor.For example, hydrogen may be stored in glass capsules that are providedto a reactor through a port in the confinement wall. In some cases,hydrogen may be provided in a pressurized form (e.g., at a pressure ofat several atmospheres) and in some cases, hydrogen may be provided inliquid form. In cases where the reactor is already in operation, thetemperature within the reactor may melt the capsule container material,allowing the fuel to be released, immediately or over a delayed period(e.g., minutes). In some cases, such as when a reactor is cool from notbeing in operation, a laser (e.g., as depicted in FIG. 22) may bedirected at a fuel capsule to break down the capsule material andrelease the reactant or fuel. In cases such as automotive applications,storing small amounts of a fusion reactant such as hydrogen in capsulesmay add convenience by reducing or eliminating hardware (e.g.,pressurized tanks) that might otherwise be required to store reactantssafely.

In some cases, a fusion reactant such as hydrogen may be introduced intothe reactor as a solid compound. For example, polymer fuel pellets madeof polyethylene or polypropylene may be provided to a reactor through aport in the confinement wall as hydrogen fuel is consumed in a reactor.Once inside a reactor, high temperatures caused by operation of thereactor or the energy of a laser (e.g., the laser as depicted in FIG.22), may be sufficient to decompose the polymer and release hydrogengas. In some embodiments, ammonia borane (also known as borazane) may beused as a hydrogen fuel. When a reactor reaches a temperature greaterthan about 100° C., the ammonia borane releases molecular hydrogen andgaseous boron-nitrogen compounds. In some cases, ammonia borane or theboron-nitrogen compounds may act as electron emitters, and in somecases, boron atoms from the ammonia borane may undergo a fusion reactionwith hydrogen atoms during operation of a reactor. In many applications(e.g., automotive applications), solid fuels may add convenience byreducing or eliminating hardware that might otherwise be required tostore gas fuels or liquid fuels safely.

Cooling System

In some cases, to enable sustained operation of the reactor, the reactormust be cooled to prevent electrodes, magnets, and/or other componentsfrom overheating. In some embodiments, a reactor may be cooled by fullemersion in a liquid bath. In some embodiments, a reactor includes aheat sink that draws heat away from the reactor via conduction andtransfers it to a fluid medium such as air or liquid coolant. As anexample, a heat exchanger may be used. A fan or a pump may be used tocontrol the flow conditions and aid in carrying away heat that istransferred to the fluid medium. Depending on the monitored temperatureswithin the reactor, the fluid velocity may be adjusted, such that fluidflow is modulated between laminar and turbulent flow. In someembodiments, fluid is passed through a cooling jacket on the outside ofa reactor and in some cases cooling tubes may be used to cool componentswithin the reactor. As described elsewhere herein, a heat sink may be aused to transfer heat to working fluid that is used by a heat engine forproducing electrical energy. Examples of liquids that may be used asworking fluids for cooling a reactor include water, liquid lead, liquidsodium, liquid bismuth, molten salts, molten metals, and various organiccompounds including some alcohols, hydrocarbons, and halocarbons.

Power Supply

Reactors may include one or power supplies that are used to supplyelectrical current to electrodes, electromagnets, and other electricalcomponents that needed to operate a reactor. The power supply maycontrol current and/or voltage between two terminals (e.g., concentricelectrodes). In some embodiments, a power supply is capable of supplyinga maximum voltage of about 200 volts to about 1000 volts. For example,in some embodiments, a power supply can provide up to 600 volts to anelectrode. In some embodiments, a small scale reactor may be able toprovide about 0.1 A to about 100 A of current and/or deliver at leastabout 1 kW of power. In some medium scale embodiments, a reactor may beable to provide about 1 A to about 1 kA of current and/or deliver atleast about 5 kW of power. In some large scale in embodiments, a reactormay be able to provide about 1 A to about 10 kA of current and/ordeliver at least hundreds of kilowatts of power.

Depending on the operating mode of the reactor, a power supply may beused to provide direct current or an alternating current. In someembodiments, an alternating current is applied to electrodes to strike aplasma. In some cases, the voltage required to strike a plasma in theconfinement region may be reduced by more than about 10% compared towhen a direct current is used to strike a plasma. In cases where an ACsignal is used to strike a plasma, a power source may deliver analternating current or voltage signal at frequencies greater than about1 kHz, or in some cases, greater than about 1 Mhz.

In some configurations, such as when an electromagnet is used to providean axial magnetic field, and alternating current may be applied to boththe electromagnet and the electrodes. In some cases, alternating signalsmay be applied to the electrodes and an electromagnet that have the samefrequency but are out of phase. In some cases, a power supply may applya current or voltage signal to an electrode or an electromagnet that isgreater than about 500 Hz, or greater than about 1 kHz. In some cases,an electromagnet is operated as the same frequency that an alternatingcurrent is applied to electrodes so that the rotation of particles maybe maintained. In some cases, a commercially available power supply maybe used to apply a current or voltage signal to the electrodes of areactor or an electromagnet. Examples of vendors of suitable powersupplies include Advanced Energy Industries and TDK-Lambda American Inc.

Sensors

When operating a reactor, a variety of parameters may be monitored tocontrol the rate of energy output, improve efficiency, prevent failureof components, and the like. For example, the temperature of a reactormay be monitored to ensure that the components of the reactor do notexceed defined maximum temperature values. If a permanent magnet getstoo hot, it may demagnetize, and if an electrode or any other componentgets too hot, it may yield or melt. In some cases, the operation of areactor requires a relatively high temperature. For example, someelectron emitters must acquire a sufficient thermal energy beforeelectrons are released into the confinement region. Temperatures withina reactor may be monitored using sensors such as thermocouples, inferredimagery, and thermistors. In some cases, temperatures at locationswithin a reactor may be inferred by measuring temperatures at otherlocations within the reactor. For example, the temperature at theinterior surface of an outer electrode may be inferred by monitoring thetemperature at the exterior surface of the outer electrode. In somecases, by measuring temperatures indirectly from an exterior location,low-cost temperature sensors, such as silicon bandgap temperaturesensors may be used.

In some embodiments, the gas pressures within the reactor may bemonitored. By monitoring the pressure in front of an electron emitter,information may be gained about the density of electrons as they arepressed tightly against the confining wall. Pressure measurements fromwithin the chamber may be used by a controller to regulate the flowrates of gas species entering and exiting the confinement region. Insome embodiments, rotational speeds within the confinement region orannular space may be monitored using a camera that captures hundreds orthousands of images per second. In some cases, measuring the rotation ofspecies within a reactor may be aided by introducing species that willfluoresce or have a detectable optical signature such as argon orquantum dots. In some embodiments, the gas composition with theconfinement region may be monitored for fusion products such as ⁴He and³He or for low quantities Deuterium within a reactant gas. In someembodiments, the detection of fusion products and reactants may beperformed using an in situ mass spectrometer (e.g., a qRGA from HidenAnalytical that is capable of detecting low quantities of Deuterium in agas sample), optical spectroscopy, or an NMR sensor. In someembodiments, a reactor may be equipped with Geiger counters to detectlevels of radiation.

FIGS. 23a-c depict an example of how nuclear magnetic resonance sensingmay be used to determine the composition of gas reactants in aconcentric electrode embodiment. FIG. 23a depicts a reactor having innerelectrode 2320, outer electrode 2310, and a substantially uniform andtime-invariant magnetic field the z-direction 2391 that passes throughthe confinement region. The axially applied magnetic field may be usedto align the nuclear spins of the rotating species and may be applied bya superconducting magnet as described elsewhere herein. In some cases,an axial magnetic field is greater than about 0.1 Tesla, in some cases,an axial magnetic field is greater than about 0.5 Tesla, and in somecases, an axial magnetic field is greater than about 2 Tesla through theconfinement region.

When detection is desired, the nuclear spins of rotating species withinthe confinement region are perturbed by applying an RF pulse in theazimuthal direction. FIG. 23b depicts how an azimuthally, time-varyingmagnetic field 2392 is generated by applying an alternating current inthe z-direction of the inner electrode. In some embodiments, thealternating current passing through the center electrode has a frequencyof between about 60 Hz to about 1 MHz, and in some cases about 1 MHz toabout 1 GHz. After perturbing the alignment of species with thetime-varying magnetic field, the rate at which the nuclear spins ofspecies are realigned is then monitored using a detection coil asdepicted in FIG. 23c . A detection coil 2390 is substantiallyperpendicular to the major axis (the z-axis) of the reactor and monitorscurrent passing through the coil as a result of the electromagneticradiation that was absorbed and re-emitted by the rotating species. Insome cases, detection coils similar to that used in a medical NMR systemmay be used.

Control System

Monitored parameters may be provided as inputs to a control system thatoperates the reactor in a regime that maintains system componentintegrity and supports fusion. The control system may control any andall parameters of the fusion reaction, and in some cases otheroperations such as heat energy gathering or utilization processes andconversion to electrical or other useful forms of energy. In certainembodiments, the control system maintains a balance between heatgeneration and heat extraction. Thus, for example, to maintain thispredetermined and preselected balance, the control system may controlapplication of electrical energy to electrodes in the reactor (e.g., bymodulating electrical pulses, e.g., lengthening or shortening the timeperiod between each pulse and/or changing the voltage applied to createthe plasma), changing the magnetic field, for example, with anadjustable magnet in conjunction with a superconducting magnet, andchanging the density of the reactants.

As discussed elsewhere herein, some parameters may need to fall within adefined process window such that both of these conditions are met. Insome cases, a control system receives information that identifies anenergy demand and adjusts process conditions accordingly. A controlsystem may also have a criterion, which when met, initiates an automatedshutdown process to prevent damage to the reactor or nearby operators.For example, if the temperature of the confining wall exceeds a certainthreshold, or radiation thresholds are reached, a reactor may quench thefusion reaction. A control system may quench a reactor by, for example,grounding all electrodes, closing gas input valves, and/or introducingan inert gas species such as nitrogen.

In some cases, a control system may provide closed-loop feedback asshown, for example, in FIG. 24. Based upon measured input parametersfrom sensors 2460 and a desired energy output signal 2461, a controlsystem 2462 may send control signals 2463 to adjust the variousparameter settings of the reactor 2464 as necessary to control theenergy output 2465 or meet other specifications. Input parameters thatare used by a controller may include parameters such as temperature,pressure, flow rates, gas composition fractions (e.g., partialpressures), particle velocities, current discharge between electrodes,and voltage. In some cases, the control system utilizes historical dataof one or more parameters. For example, while it may be important toknow a particular temperature value, it may also be important tounderstand the rate and/or magnitude at which temperature isfluctuating. Examples of reactor settings that may be adjusted by thecontroller include applied currents, applied voltages, applied magneticfield strength (in the case of an electromagnet), and gas flow rates(e.g., hydrogen flow rates). Typically, the controller passes a controlsignal to a reactor component responsible for the associated setting.For example, a control signal may be passed to a power supply toinstruct the power supply to apply a specified voltage. In some cases, asetting may also be an input parameter to the control system. Forexample, in determining what voltage should be applied, a controller mayaccount for the current and/or voltage presently applied to theelectrodes. In some cases, a controller may use machine learning toimprove its decisions so that a reactor may become more efficient overtime, resistant to physical changes in the device (e.g., when a partfails and is replaced), or anticipate energy demand.

Certain operational features of a reactor may be independentlycontrolled. For example, the flow rate of a cooling fluid may becontrolled using a system that is independent of the control systemresponsible for adjusting the primary operating inputs of a reactor,such as current and gas flow rates. In another example, electronemitting modules, e.g. as depicted in FIG. 21a , may have an associatedcontroller that receives a measured temperature of the electron emitterand determines what current should be applied to a filament to provideJoule heating.

The control system described above may be implemented in the form ofcontrol logic using computer software in a modular or integrated manner.There are many possible ways to control operation. Based on thedisclosure and teachings provided herein, a person of ordinary skill inthe art will appreciate how to implement the control functions usinghardware and/or a combination of hardware and software.

In some cases, a control system may be implemented as software code tobe executed by a processor using any suitable computer language such as,for example, Java, LabVIEW, MATLAB, C++, or Python using, for example,conventional or object-oriented techniques. The software code may bestored as a series of instructions, or commands on a computer-readablemedium, such as a random access memory (RAM), a read-only memory (ROM),a magnetic medium such as a hard-drive or a floppy disk, or an opticalmedium such as a CD-ROM. In some cases, a control system may be testedand designed using a FPGA (Field Programmable Gate Array), and thenlater manufactured through an ASIC process. In some cases, a controllermay be a single chip that can securely store and execute the controllogic. Any such computer readable medium may reside on or within asingle computational apparatus and may be present on or within differentcomputational apparatuses within a system or network. For example, thecontrol system may be implemented using one or more processors, PLCs,computers, processor-memory combinations, and variations andcombinations of these. The control system may be a distributed controlnetwork, a control network, or other types of control systems known tothose of skill in the art for controlling large plants and facilities,and individual apparatus, as well as combinations and variations ofthese.

Radiation Shield

In some embodiments, such as when a reactor supports an aneutronic orsubstantially aneutronic reaction, the reactor may require little if anyshielding to reduce radiation exposure. When there is a concern ofneutronic radiation, the reactor may be outfitted with appropriateshielding. Neutrons readily pass through most material but interactenough to cause biological damage. In some cases, a reactor may beplaced in an enclosure that absorbs neutrons. In some cases, theconfinement wall of a reactor may include an external layer forabsorbing neutrons. In some cases, shielding layers may be made ofconcrete having a high water content, polyethylene, paraffin, wax,water, or other hydrocarbon materials. In some cases, a shielding layermay include a lead or boron as a neutron absorber. For example, boroncarbide may be used as a shielding layer where concrete would be costprohibitive. In some embodiments, the ends of a reactor in thez-direction may include a material such as boron nitride that not onlyabsorbs neutrons but is thermally and electrically insulating. In somecases, an electron emitter, such as lanthanum hexaboride, serves theadditional function of providing shielding from neurotic radiation. Insome cases, such as large scale reactors, tanks of water, oil, orgravel, may be placed over a reactor to provide effective shielding. Thethickness of a shielding layer depends in part of what materials areused, where the reactor is located, the type of fusion reaction, and thesize of the reactor. In some embodiments a shielding layer is greaterthan about 10 centimeters, in some cases, a shielding layer is greaterthan about 100 centimeters, and in some cases, a shielding layer isgreater than about 1 meter.

Replaceable Components

Due to the aggressive nature of the plasma and fusion products within areactor, electrodes may become damaged, distorted, embrittled, etc.Under normal operating conditions, some components of a reactor mayeventually fail and need to be replaced. Further, when operatingconditions exceed certain thresholds (e.g., high temperatures,pressures, plasma potentials, or reactant concentrations), componentsmay be damaged or wear out more quickly. In cases where hydrogen is usedas a reactant, electrodes may, over time, suffer from hydrogenembrittlement. If an embrittled electrode is not replaced, it ispossible for the electrode to convert into a powder. In some cases, areactor may be inadvertently operated outside its normal operatingconditions resulting in increased wear or structural damage to one ormore electrodes or other components. For example, if a cooling systemmalfunctions, the temperature of an electrode may near its meltingtemperature causing the electrode to deform. In some cases, thermalstresses may cause micro-fractures to appear on or within an electrode.If an electrode has an internal cooling system that breaches to allowwater vapor to enter into the confinement region, the reactor mayexperience a spike in the pressure.

Fusion reactors as described herein may be highly configurable andmodular. In certain embodiments, one or more components may be replacedand/or interchanged. Some components are permanent and are designed tonot wear out during a reactor's lifetime, and some components areexpected to be replaced after a certain number of operation cycles ortime in operation. For each replaceable component, there may be adesignated procedure for the removal, handling, refurbishment, and/orreplacement of the component. In addition, there may be one or moreindicators and field-implementable diagnostics that indicated and/oranticipate the degradation of the component.

Examples of replaceable components include one or more electrodes in thereactor, fusion reactants, containers fusion reactants (e.g. hydrogengas canisters), and energy conversion devices associated with thereactor.

Examples of indicators that a component should be replaced include adecrease in electrical conductivity of an electrode, the time thecomponent has been in operation, and the optical properties of thecomponent (e.g., changes to the surface of a component may be detectedoptically). Mechanical failure may be determined by visual inspection,or in some cases, by monitoring measured parameters such as temperature,pressure, and conductivity of the electrodes. In some cases, a controlsystem contains logic for determining a mechanical failure of anelectrode or other component.

In some cases, the conductivity and/or conductance of electrodes maydecrease over time. Due to the volatile nature of plasma, there can bean electrically insulative dielectric coating that forms on theelectrode. If the conductivity and/or conductance of an electrode isreduced, the reactor may become less efficient and/or require excessamounts of power. If nothing is done to mitigate the decliningconductance and/or conductivity of a reactor, the reactor may become anelectrical and/or thermal hazard. While much of the discussion hereinconcerns determining an electrode's conductivity and/or conductance, itshould be understood that conductivity may vary fromposition-to-position in an electrode. For example, the conductivity ofthe reaction-facing surface of an electrode may be much lower, after along period of operation, than the conductivity of an interior portionof the electrode. As another example, the conductivity of the originalmaterial in an electrode may remain largely unchanged during operation,but a dielectric film formed on the reaction-facing surface of theelectrode may significantly degrade the overall conductance of theelectrode. Resistivity and/or resistance can be determined in lieu ofconductivity and/or conductance.

Various techniques may be employed to monitor electrode conductivityand/or conductance or determine that electrode conductivity orconductance has reached a level that requires attention or replacement.In one example, using the electrode's geometry, the conductivity of theelectrode may be determined by measuring the resistance between twopoints on the electrode surface when the reactor is not in operation.This measurement may be performed manually during a routine systemcheck, e.g., by using a multimeter. In some cases, a reactor isconfigured with measurement circuitry that automatically measures theresistance of an electrode between operation cycles. In some cases, areactor's control system may be configured to automatically determinethe conductance of an electrode from a measured resistance. Another wayan electrode's conductance may be determined is by performing adiagnostic cycle in which a gaseous reactant in the confinement regionis replaced with another gas, and a plasma is generated within theconfinement region. For example, hydrogen gas may be replaced with argongas, neon gas, or nitrogen gas. A control system may then monitor theelectrical behavior of the plasma measuring the voltage of theelectrodes and the current passing through the electrodes. Based uponthe electrical behavior of the argon plasma, the conductivity of anelectrode may be determined. For example, the conductivity of eachelectrode may be determined by comparing the measured electricalbehavior of the argon plasma (or another plasma) to an expectedelectrical behavior. In some cases, the expected electrical behavior ofa plasma, such as an argon plasma, may be determined via simulation, orby measuring the electrical behavior on a new reactor that does not havea dielectric coating.

A reactor electrode may be assigned a predetermined threshold of lowconductivity or conductance value that triggers service or replacementof an electrode. For example, if the conductivity of an electrode fallsbelow about 80% of its expected value, the electrode may be replaced ortreated to restore conductivity to an appropriate level.

In some embodiments, when an electrodes conductivity or conductancefalls below and acceptable level, a cleaning cycle is performed. Forexample, a cleaning cycle may involve introducing a cleaning gas, e.g.argon, into the confinement region and operating the reactor to generatea plasma that removes some or all of the dielectric coating. In somecases, a weakly ionized plasma may be sufficient to remove thedielectric coating. In some cases, the argon gas may be fully ionizedduring a cleaning cycle. Depending on the chemical nature of thedegradation, a chemically restorative treatment may be employed. Forexample, if the electrode degradation results from the formation of ahydride or other form of hydrogen-mediated reduction, the compromisedelectrode may be treated with an oxidizing agent, such as anoxygen-containing plasma.

In some cases, if the conductivity or conductance of an electrode fallsbelow a designated level (e.g., about 50% of its expected value), thereactor may be determined to be unsafe to operate. This may beindicative that a thick dielectric film has formed and the reactor willrequire dangerous levels of power from a power source. In some cases, acontrol system or associated safety system may shut down operation untilreplacement or restoration of an affected electrode. In some cases, areactor's control system contains logic for determining a mechanicalfailure of an electrode or other component and then triggering an alertor automatic shutdown of the reactor.

In some embodiments, one or more of the electrodes or magnets in areactor include a protective or sacrificial layer. In some cases, thissacrificial layer is a sleeve (e.g., a sleeve that forms the interiorsurface of the confining wall) that may be replaced at scheduledintervals. In some embodiments, a metal component such as an electrodeor a sleeve may be removed to undergo a restorative process, e.g. anannealing process to remove internal stresses that may have arisen dueto thermal cycling. In some cases, e.g., when component experienceshydrogen embrittlement, the component may be removed and the material ofthe component may be reprocessed to make a new part. In some cases, anembrittled component, e.g. a tantalum electrode, may be restored to aductile condition by annealing under a vacuum. For example, in somecases, an embrittled component may be restored by annealing at around1200° C. under a vacuum.

Target materials (fusion reactants) may eventually be consumed and needto be replaced. For example, some embodiments employ lanthanumhexaboride which contains boron-11 as a reactant required for aproton-boron-11 fusion reaction. Once depleted, this material needs tobe replaced. Due to thermal cycling, lanthanum hexaboride may alsobecome brittle and fail. Destruction or degradation of lanthanumhexaboride will reduce the fusion reaction output. In some cases, acontrol system may notify an operator of a power drop-off that wouldcorrespond to a target material being depleted or moved out of theconfinement region. In some cases, a control system may alert anoperator when a consumable material like lanthanum hexaboride hadreached a predetermined use limit and should be replaced.

EXAMPLES

The following non-limiting examples represent a few embodiments that maybe practiced in accordance with the broader principles described herein.

1.) Negative Electrode (Outer Electrode)

The outer electrode, sometimes called the “shroud” includes acylindrical metal ring with multiple points of attachment for thelanthanum hexaboride or other target material. The composition of theshroud is typically a refractory metal, such as tantalum (Ta) ortungsten (W), due to the high thermal resistance of refractory metals;however, certain embodiments of the reactor use lower temperature metalssuch as Alloy 316 Stainless Steel. These embodiments may include aliquid cooling circuit that prevents the shroud from reaching thecritical melting temperature of the composition metal. As explained, theouter electrode may be either the more negative or the more positiveelectrode.

Electrical Conductivity

The plasma in the reactor is struck between the positive electrode andthe negative electrode by utilizing electrical power from an externalpower supply. This event is mediated by the electrical voltage acrossthe two electrodes and the electrical current traveling through theelectrodes and the plasma. The voltage required to strike the plasma andinitiate the fusion process may be directly related to the electricalconductivity of the two electrodes. As mentioned, there can be adielectric (electrically insulative) coating that builds up on thenegative electrode, thus affecting the electrical conductivity of theelectrode.

A field-implementable diagnostic for determining conductivity of theouter electrode is a resistance measurement between two points using adigital multimeter. In some implementations, once the resistance ismeasured, its value is entered into QA software, which will indicate theconductivity and operational status of the outer electrode.

A second diagnostic for determining conductivity would involve thestriking of an glow discharge argon plasma in the reactor. This is donevia control software, which will subsequently monitor the electricalbehavior of the argon plasma (voltage and current). By an automaticcomparison to an internal calibration, the control software candetermine the conductivity of the electrode and send the data to QAsoftware.

If the QA software indicates that the electrical conductivity fallsbelow 80% of the standard conductivity rating of the composition metal,then the AR unit is said to be outside of the optimal operation regimeand into the non-optimal operation regime. If the conductivity fallsbelow 50% of the standard rating, then the AR unit is said to be in theunsafe operation regime, as this will draw too much power from the powersupply and provide a potential electrical and thermal hazard. If theconductivity is 0%, this indicates that a complete insulative layer hasformed on the negative electrode and the system is non-operational.

Operation: Continue operating unit normally.

Non-optimal operation: Run Argon Cleaning Cycle on AR unit usingprovided control software. Repeat until conductivity enters ‘optimaloperation’ zone. If conductivity does not improve, perform the ‘unsafeoperation’ below.

Unsafe operation: The outer electrode should be cleaned.

Structural Integrity

It is possible for the mechanical structure of the shroud to becomedamaged, distorted, or embrittled. This can occur due to a number ofdifferent reasons.

A failure in the cooling system, or improper operation of the coolingsystem, can lead to extreme temperatures inside the reactor that arebeyond the safe operating parameters. These extreme temperatures canlead to thermal shock, causing micro-fractures to appear on or withinthe shroud. Additionally, if these extreme temperatures approach themelting point of the shroud composition material, the shroud itself willbegin to distort and melt.

A field-implementable diagnostic for detecting defects in structuralintegrity is visual inspection prompted by an abnormal temperature alertfrom the control software. The control software may monitor thetemperature of several different components of the unit, and check thateach component remains within safe operating parameters. If thetemperature of any such component travels outside the safe operatingparameters, it may trip a temperature indicator alarm. In extreme cases(such as a prolonged duration of an overheated component), the systemmay shut itself down and require a mandatory visual inspection of theintegrity of the shroud. If the shroud is damaged, it may be sent to aQA team for inspection and analysis.

2.) Positive Electrode (Inner Electrode)

The inner electrode may includes a cylindrical metal disk and hollowmetal cylinder attached to a high-voltage ceramic feedthrough on theback of the chamber. These two components are known as the ‘head’ andthe ‘rod.’ The composition of the center electrode head is typically arefractory metal, such as tantalum (Ta) or tungsten (W), due to the highthermal resistance of refractory metals; however, different embodimentsof the reactor use lower temperature metals such as Alloy 316 StainlessSteel. Higher-temperature center heads will operate longer and thus willwarrant replacement less frequently. The center electrode rod istypically made of Alloy 316 Stainless Steel, since it does notexperience the same extreme temperatures as the head.

In some embodiments, the center electrode rod is cooled with liquidwater to prevent overheating. In embodiments utilizing ahigh-temperature head, the head is attached to the rod with a Molybdenum(Mo) set screw. In embodiments utilizing a low-temperature head, thehead is also water cooled, and it is welded or soldered to the rod suchthat the cooling circuit is continuous.

Electrical Conductivity

As in the case for the outer electrode, the electrical conductivity ofthe inner electrode mediates the electrical behavior of the plasma. Achange in the conductivity will result in the change of the voltagerequired to strike and sustain the plasma for the fusion reaction. Asmentioned above, the volatile nature of the plasma and fusion reactionstaking place inside the reactor can lead to the build-up of a dielectriccoating on the surface of the inner electrode, thus affecting itselectrical conductivity.

The standard field-implementable diagnostics for determining theelectrical conductivity of the center electrode (with respect to thevarious operational regimes outlined above) are identical to those forthe inner electrode.

Structural Integrity

The inner electrode has the same operational risks as the outerelectrode (or shroud) with regards to the structural integrity of thecomponent. It can be damaged, distorted, or embrittled; however, sincethere is a liquid cooling channel inside the inner electrode, there areadditional methods for failure detection other than the thermalmonitoring of specific components by the control system.

If the temperature of the center electrode rod (or the temperature ofthe liquid-cooled center electrode head described above as an alternateembodiment) approaches the melting temperature of the compositionmaterial, the outer surface of the rod (or head) may be breached,allowing a combination of water vapor and liquid water into the vacuumchamber. This can occur due to a failure of or improper use of thecooling system, as well as the appearance of a sustained plasma arc onthe center electrode rod (or head) itself. Once this occurs, there willbe an instantaneous rise in pressure due to the preponderance of watervapor entering the chamber through the breach. The control system willdetect this pressure rise and immediately shut the system down with anerror fault that warrants an immediate and required visual inspection.

3.) Lanthanum Hexaboride Target

Lanthanum Hexaboride, commonly referred to as LaB₆, is a refractoryceramic material that is used in the scientific industry as an electronemitter due to its low work function. In a reactor, the LaB₆ is attachedto the negative electrode via uniformly distributed attachment pointsalong the inner wall. The LaB₆ contains the solid boron fuel requiredfor a fusion reaction, and will need to be replaced once the fuel isdepleted.

Boron Isotope Composition

There are two main isotopes (atoms of same number of protons anddifferent number of neutrons) of boron found in nature, ¹⁰B, and ¹¹B.The most abundant of these two isotopes is ¹¹B, as 80% of all Boron isfound in this form. Since this is also the isotope required for thefusion reaction to take place, it may be necessary to know the relativeconcentration of this particular isotope present in the LaB₆ fuel. Thereare various methods for detective this concentration, includinginductively coupled plasma optical emission spectrometry (ICP-OES),thermal ionization mass spectrometry (TIMS), secondary ion massspectrometry (SIMS), inductively coupled plasma mass spectrometry(ICP-MS), among others.

In some embodiments, there is not field-implementable diagnostic that isable to measure the boron isotope composition of the LaB₆, as these aretechniques that require the sample to be sent to a third-partyanalytical diagnostics lab.

Structural Integrity

Due to the ceramic nature of this compound, it is extremely brittle, andis extremely susceptible to thermal stress. The volatile reactionsoccurring inside the reactor, as well as the rapid rates of heating andcooling present in various components such as the center electrode andthe shroud, can cause the structural integrity of the LaB₆ to breakdown. It has been observed in several embodiments of the reactor thatthe LaB₆ fuel will tend to break apart over time, which warrants theneed for replacement.

One field-implementable diagnostic for determining the structuralintegrity (and lack thereof) of the LaB₆ fuel is by visual inspection.There are certain indicators provided by the control software thatwarrant the need for a visual inspection of the LaB₆. Because the fusionreactions occur at the LaB₆ sites, the entirety of the output power (asmeasured by the control software) is extracted from these sites. If thesteady-state power output of the reactor drops by more than 20%, itcould indicate a problem with one of the LaB₆ pieces and trip a powerindicator alarm on the software. This type of alarm would warrant theneed for a visual inspection of the LaB₆ pieces.

Energy Conversion Hardware

Reactors, as described herein, produce energy in one or more forms;typically they produce multiple forms of energy simultaneously. Whenoperating, most reactors produce thermal energy. They may also produceradiant energy over a broad or narrow range of frequencies. For example,excited species within the reactor (e.g., electronically excitedhydrogen atoms) emit radiation in one or more frequency bands. Often thereactor operates in modes that require plasma and/or produce a plasma,and when the plasma exists, it produces radiant energy. Still further,many reactions produce charged species (e.g., ions such as alphaparticles) with high levels of kinetic energy. Reactors may also producemechanical energy through pressure variations or oscillations.

Any one or more of these energy forms may be converted to differentenergy forms usable for particular applications. Therefore, in certainembodiments, an energy conversion device or component is coupled to anassociated reactor. In some cases, the energy conversion device convertsthermal energy from the reactor to electrical energy (e.g., athermoelectric device). In some cases, the energy conversion deviceconverts thermal energy from the reactor to mechanical energy (e.g., aheat engine). In some cases, the energy conversion device convertselectromagnetic radiation from the reactor to electrical energy (e.g., aphotovoltaic device). In some cases, the energy conversion deviceconverts the kinetic energy of charged reaction products (e.g., alphaparticles) or ionized fusion reactants (e.g., protons) to electricalenergy. In some cases, the energy conversion device converts mechanicalenergy from the reactor to electrical energy (e.g., a piezoelectricdevice).

Various energy conversion devices may be used to convert thermal energyproduced by reactor into mechanical and/or electrical energy. Forexample, a thermoelectric generator may be thermally coupled to areactor to generate electrical energy. A thermoelectric generator may bethermally coupled to the reactor by, for example, being placed on theconfinement wall of the reactor or having thermal energy from thereactor delivered via a heat transfer device such as a heat pipe. Inanother example, a reactor may convert thermal energy into mechanicalenergy (e.g., a moving piston or a rotating crankshaft) via a heatengine. In some embodiments, a reactor is outfitted with a Stirlingengine. In some embodiments, the reactor may be outfitted with a heatengine, e.g., a heat engine that uses the Rankine cycle, where theworking fluid experiences cyclic phase changes. If electrical energy isdesired, a heat engine may be configured with an electric generator thatconverts, for example, a rotating crankshaft or an oscillating pistoninto electrical energy.

Some energy conversion devices may convert electromagnetic radiation orradiant energy produced by reactor into electrical energy. For example,a reactor may have photovoltaic cells on either end of the confinementregion to convert radiant energy into electrical energy. In some cases,the reactor may include a transparent barrier to provide thermalprotection and/or optical devices to concentrate the radiant energy ontoa photovoltaic cell. In some cases, a photovoltaic cell may have a tunedbandgap corresponding to a narrowband wavelength of radiant energy(e.g., corresponding to hydrogen) emitted from the reactor.

The reactor may also be configured with components that convert thekinetic energy of charged particles emitted from a reactor intoelectrical energy. For example, positively charged particles (e.g. alphaparticles) may be forced to travel through an opposing electric fieldgenerated by one or more electrodes that slow their travel. As theparticles decelerate, an electric current is generated in an electricalcircuit connected to the positively charged electrode(s). In some cases,alpha particles emitted from the reactor may be directed towards suchelectrodes via applied magnetic fields. In some cases, the reactor maybe configured with a magnetohydrodynamic generator (MHD generator) thatconverts the kinetic energy of a plasma generated as a result of anuclear reaction into electrical energy.

In some cases, the reactor may use a single energy conversion device (orenergy conversion modules) to convert energy produced by the reactorinto mechanical and/or electrical energy. In some embodiments, thereactor may use a plurality of energy conversion devices (or energyconversion modules) to convert energy produced by the reactor intomechanical and/or electrical energy. Since the reactor may producevarious forms of energy, different types of energy conversion devicesmay be combined to increase the total mechanical and/or electricalenergy that is generated. In some cases, the addition of a second energyconversion device may not reduce the energy output of a first energyconversion device because the energy conversion devices convertdifferent forms of energy produced by the reactor. For example, in someembodiments, the reactor may generate electrical energy from both aphotovoltaic cell which converts radiant energy and a thermoelectricgenerator which converts thermal energy. In this example, the presenceof a photovoltaic cell may not diminish the electrical energy producedby the thermoelectric generator and vice versa. In some embodiments, areactor may be outfitted with multiple energy conversion devices thatconvert the same type of energy produced by the reactor. For example, insome cases, a reactor may be outfitted with a Stirling engine as well asa thermoelectric generator both of which make use of thermal energy. Inthis example, a thermoelectric generator may simply capture the thermalenergy that was not converted to mechanical and/or electrical energy bythe Stirling engine. In general, any combination of energy conversiondevices or modules described in herein may be used to generatemechanical and/or electrical energy from a reactor.

Enclosure

While not depicted, a reactor may include an enclosure that walls offthe confinement region from the ambient environment. In some cases, thedimensions of an enclosure are governed in part by the outer dimensionsof a confining wall. In some embodiments, the confining wall defines theboundary of the enclosure in the r-direction, and the confinement regionis isolated from the external environment using flanges on both ends ofthe confinement wall in the z-direction. In some embodiments, an entiresystem including control systems, power supplies, magnets, and energyconversion apparatuses is placed within an enclosure. Materials chosenfor an enclosure may depend on the enclosure's intended purpose. Forexample, enclosures may be needed to provide biological shielding,thermal isolation, and/or to enable low-pressure operating conditions.In some cases, an enclosure may have a layered structure in which eachlayer provides a different function. For example, an enclosure mayinclude a hydrocarbon material for biological shielding and a ceramiclayer to provide thermal insulation. In some cases, more than oneenclosure may be used. For example, a first enclosure may includeflanges that seal off the confinement region in the z-direction creatinga vacuum chamber while a second, exterior enclosure encompasses theentire reactor. Based on the disclosure and teachings provided herein, aperson of ordinary skill in the art will know and appreciate ways and/ormethods to implement an enclosure to that meets the needs of a reactor'sapplication.

Process Conditions

Multistage Operations and/or Reactions

In some cases, the energy output or efficiency of a reactor is improvedwhen operated in multiple stages. In some cases, a reactor may have oneor more preparatory stages that prime the conditions within a reactorfor conducting a fusion reaction. For example, preparatory stages in amultistage process may be used to increase the temperature of electronemitters, cool the temperature of a confining wall, generate a plasmawithin the confinement region, or modify the gas pressure within theconfinement region. FIG. 25 depicts an example of a multistage processflow that may be used to operate a reactor. In a first operation, 2501,electron emitters are heated until they reach a prescribed temperaturefor emitting electrons. After heating the electron emitters in 2501, analternating current is applied between the electrodes of the reactor tostrike a weakly ionized plasma.

Immediately after initiating a plasma in the confinement region, thereactor may transition to a stage used to rotate charged particles inthe reactor and sustain a fusion reaction. In some Lorentzian rotors,this may mean applying a direct current to the electrodes when a uniformmagnetic field is applied. Alternatively, in embodiments in which analternating magnetic field is applied in the z-direction of a reactor,this may mean applying an alternating current to the electrodes at thesame frequency that the magnetic field oscillates. In some cases, analternating magnetic field may be applied by applying an alternatingcurrent to an electromagnet (e.g. a superconducting magnet) orphysically moving permanent magnets by, e.g., by having rotors havingmagnets with alternating magnetic orientations on either side of theconfinement region. In some cases, the rotation of neutrals and chargedparticles is maintained in the same direction by alternating theelectric field and the magnetic field at the same frequency. Forexample, in some cases, the both the electric and magnetic field may beoscillated at a frequency that is between about 0.1 Hz and 10 Hz, insome cases, about 10 Hz to about 1 kHz, and in some cases greater than 1kHz.

In a wave-particle embodiment, a sequence of electrode charges, or adrive signal, may be applied to the electrodes bordering the confinementregion to initiate rotation. For example, a drive signal may be starteda low frequency, e.g. about 60 Hz and then ramp up to a higher frequencye.g. about 10 MHz. In some cases, a reactor may include a similarmultistage process for terminating a fusion reaction. In some cases, areactor may have an idle stage of operation that occurs between whenfusion reaction is halted and then resumed. During operation of areactor, the parameters may be closely monitored. In a reactor thatmakes use of a Lorentz force to rotate charges species, the currentdensity in the confinement region or annular space near the confiningwall may be in the range of about 150 A/m² to about 10 kA/m², e.g.,about 150 A/m² to about 9 kA/m². In some cases, the current density neara confining wall may be in the range of about 150 A/m² to about 700kA/m², and in some cases in the range of about 400 A/m² to about 6000kA/m². In some cases a reactor is operated to maintain a sufficientelectric field near the confining wall. For example, in some cases theelectric field is greater than about 25 V/m, in some cases greater thanabout 40 V/m, and in some case greater than about 30 V/m.

In some multistage operations, a reactor may periodically alternate thedirection in which charged particles are rotated. In some cases, byalternating the direction that charged particles rotate, the rate ofcollisions between two rotating fusion reactants may be increased. Insome cases, the direction of rotation may be alternated to increase orcontrol the rate of fusion in a reactor. In some embodiments, byalternating the direction of rotation the rate of fusible events on aconfinement wall may be reduced due to fusible events occurring withinthe annular space rather than on the confinement surface. This may bebeneficial to, for instance, reduce heat imparted to a confinement wallif the confinement wall becomes too hot. In the cases of Lorentzianrotors, the direction of rotation may be alternated by alternating anapplied electric field and/or magnetic field. For example, if themagnetic field is alternated while an electric field is maintained, theLorentzian force on charged particles will also alternate directions. Insome cases, an applied electric field and or an applied magnetic fieldis alternated at a frequency between about 0.1 Hz to about 10 Hz, insome cases, about 10 Hz to about 1 kHz, and in some cases greater thanabout 1 kHz. This may have the effect of concentrating electrons in theelectron-rich region, concentrating rotating particles in closeproximity, and in some cases, increasing the number of fusion reactions.

Gas Conditions

In cases where gas is introduced into the confinement region, e.g. ahydrogen or helium reactant gas, it may be beneficial for the reactantgas to have certain purity. In some cases, impurities in a reactant gasvolume may decrease the rate of fusion and the overall energy output. Incases where a reactant gas is readily available in a pure form, areactant gas having a purity of at least about 99.95% by volume or atleast about 99.999% by volume. This means there are fewer than 10 vpm(volume per million) impurities in the cylinder.

In some cases, deuterium, a naturally occurring isotope of hydrogen, maybe found within a hydrogen reactant gas. For example, deuterium may bepresent within the impurities of a hydrogen tank, and as such, present apotential hazard when present in sufficient quantities within thereactant gas. If there is too much deuterium in the fuel, fusionreactions other than proton-boron¹¹ may occur within the reactor. Insome instances, these other reactions may emit radioactive byproducts.To monitor the amount of deuterium in a reactant gas, a reactor may beequipped with sensors, such as the qRGA from Hiden Analytical massspectrometer, for monitoring the amount of deuterium within a hydrogenreactant gas.

Prior to ignition, a reactor may contain a mole fraction of ions toneutrals that is close to 0%. After striking a plasma, the reactor maybe operated having a mole fraction of ions to neutrals in the rotatinggas species that is about 1:1000 to about 1:1,000,000. In some cases,the mole fraction of ions to neutrals in a reactant gas may varydepending on the particular stage of a multistage process flow. Forexample, in the process flow of FIG. 25, a gas may have a higher molefraction of ions to neutrals after initiating a plasma in stage 2502than while the reactor is operating at steady state in stage in 2503.

As described elsewhere, reactors may be equipped with gas inlet and exitvalves. In principle, the flow through a gas inlet valve and/or a gasoutlet valve may be controlled to maintain a desired gas composition orgas pressure within the confinement region. In some cases, the gasvolume in the confinement region may be replaced at a rate that is lessthan about once a minute, or about once an hour. In many embodiments,gas valves may be sealed, so there is no fluid flow during operation ofthe reactor.

In some cases, a reactant gas is maintained at standard temperature andpressure before generating a plasma in the confinement region. In somecases, such as when a vacuum enclosure is used, a vacuum pump may beused to lower the pressure to less than about 1×10⁻² Torr, and in somecases less than about 1×10⁻⁶ Torr prior to striking a plasma in theconfinement region. In some cases, to increase the density of neutrals areactant gas feedline may increase the pressure within a reactor to morethan about 0.1 Torr, and in some cases more than about 10 Torr beforestriking a plasma in the confinement region or during operation of areactor. During operation of the reactor, particles may experience acentripetal acceleration that is on the order of a billion times that ofthe gravitational acceleration on the surface of the earth. In somecases, the gas pressure and/or density along the confinement wall may bemonitored during operation of the reactor. If the pressure induced therotating species is not sufficient near the confining wall, the electronrich region may diffuse farther into the confinement region and notprovide the desired electron screening effect. In some cases, the gaspressure near the confinement wall may be monitored in real time. Priorto initiating a plasma the temperature of a gas may be approximately atroom temperature, in some cases a gas is initially heated. In somecases, the gas is heated to greater than about 1,800° C., and in somecases the gas is heated to greater than about 2,200° C. During steadyoperation of the reactor the gas temperature may me heated such that thegas in the confinement region is in the range of about 400° C. to about800° C., and in some cases in the range of about 900° C. to about 1,500°C.

As discussed elsewhere, a reactant gas may be delivered into a reactorby a variety of mechanisms. In cases in which as inlet valve is used, agas reactant may be delivered from a gas canister or pressurized tank.In some embodiments, a reactant gas such as hydrogen may be deliveredinto the confinement region by being out-diffused from the confinementwall or a hydrogen absorbing material such as titanium or palladium.

Operating Conditions for Reducing Coulombic Barrier

As described elsewhere herein, the rate of fusion per volume per unittime may be expressed by

dN/dT=n ₁ n ₂ σ v

where n₁ and n₂ are the densities of the respective reactants, σ is thefusion cross section at a particular energy, and v is the relativevelocity between the two interacting species. The product (σ v) may beincreased by reducing the coulombic barrier. In some cases, the fusioncross section may be between about 10⁻³⁰ cm² and about 10⁻⁴⁸ cm², and insome cases about 10⁻²⁸ cm² and about 10⁻²⁴ cm². In some cases, therelative velocity is between 10⁴ m/s and 10⁶ m/s, and in some casesbetween about 10³ m/s and about 10⁴ m/s. In some cases, a reduction tothe coulombic barrier may result in a reaction rate that is about 10¹⁷to about 10²² fusion reactions per second per cubic centimeter along theconfinement wall.

As discussed elsewhere, an electron-rich region may be formed near theconfinement wall to provide a screening effect between colliding nuclei.In some cases, electron emitters may be used to provide free electronsto this region. Emitters may be energized optically (e.g., using alaser), by frictional heating of the rotating particles, and/or by Jouleheating.

Within the electron-rich region, the density of electrons may be onorder of about 10¹⁰ cm⁻³ to about 10²³ cm⁻³, and in some cases, thedensity of electrons is on the order of about 10²³ cm⁻³ within thisregion. In some embodiments, the density of neutrals in theelectron-rich region may be about 10¹⁶ cm⁻³to about 10¹⁸ cm⁻³, and insome cases, the neutrals density within the confinement region is on theorder of about 10²⁰ cm⁻³. Positive ions may be found at a much lowerdensity than neutrals within the electron-rich region. In some cases,the density of positive ions is about 10¹⁵ cm⁻³ to about 10¹⁶ cm⁻³. Insome cases the ratio of electrons to positive ions within theelectron-rich region is in the range of about 10⁶:1 to about 10⁸:1.

The radial thickness of the electron-rich region may be characterized asthe region in where most of the electron gradient exists. In some cases,the electron-rich region is in the range of about 50 nm to about 50 um,in some cases, the electron rich is about 500 nm to about 1.5 um.

Within the electron-rich region, e.g. about 1 um away from the confiningwall, there may be a strong electric field. In some cases, the electricfield within the electron-rich region (or confinement region) is greaterthan 10⁶ V/m, and in some cases, the electric field is greater thanabout 10⁸ V/m. In some cases, the temperature of electrons in thisregion is about 10,000 K to about 50,000 K, and in some cases about15,000 K to about 40,000 K.

In some cases, if one parameter is constrained by a physical limitation,that parameter may end up being a driving parameter that affects otherparameters within the electron-rich region. For example, the Lawsoncriterion involves a balance of parameters.

In some cases, the parameters of the electron-rich region may depend inpart on the fusion reaction that is targeted. For example, the parameterranges are different in a p+¹¹B reaction vs. a D+D reaction.

Another approach to increasing the probability of fusion events is byaligning the spin of the fusion reactants. The nuclear force has aspin-dependent component. When spins are aligned, between two nuclei,e.g., those of a deuteron and a deuteron, the coulombic barrier isreduced. Nuclear magnetic moments play a role in quantum tunneling.Specifically, when the magnetic moments of two nuclei are parallel, anattractive force between the two nuclei is created. As a result, thetotal potential barrier between two nuclei with parallel magneticmoments is lowered, and a tunneling event is more likely to occur. Thereverse is true when two nuclei have antiparallel magnetic moments, thepotential barrier is increased, and tunneling is less likely to occur.When the magnetic moment of a particular type of nucleus is positive,the nucleus tends to align its magnetic moment in the direction of anapplied magnetic field. Conversely, when the moment is negative, thenucleus tends to align antiparallel to an applied field. Most nuclei,including most nuclei which are of interest as potential fusionreactants, have positive magnetic moments (p, D, T, ⁶Li, ⁷Li, and ¹¹Ball have positive moments; ³He and ¹⁵N have negative moments). Incertain embodiments, a magnetic field is provided that aligns themagnetic moments in approximately the same direction at every pointwithin the device where a magnetic field is present. This results in areduction of the total potential energy barrier between nuclei when thefirst and second working materials have nuclear magnetic moments whichare either both positive or both negative. It is believed that thisleads to an increased rate of tunneling and a greater occurrence offusion reactions. This effect may also be referred to as spinpolarization or magnetic dipole-dipole interaction. In addition, thegyration of a nucleus about a magnetic field line also contributes todetermining the total angular momentum of the nucleus. So when thecyclotron motion of the nucleus produces additional angular momentum inthe same direction as the polarization of the nuclear magnetic moment,the Coulomb barrier is further reduced.

In some cases, the spin states of fusion reactants (e.g., ¹H and ¹¹B) inthe confinement region and along the confining wall may be aligned byapplying a magnetic field in the range of 1-20 T. In cases in which amagnetic field is used to provide a Lorentzian force, the magnetic fieldmay also align the spin states of the fusion reactants. The combinationof a reduced coulombic barrier through, e.g., electron screening and aspin polarization (enabled by a strong magnetic field acting on thereactant nuclei) may produce a significant enhancement in the ratefusion. The electrostatic attraction between two nuclei includes aspin-dependent term that becomes dominate at short distances (e.g., lessthan 1 fm).

Applications

Fusion reactors as described herein have abundant applications that mayresolve many societal issues such dependence on fossil fuels. In somecases, the use of fusion reactors may make feasible and/or practicalenergy intensive applications that were not feasible or practical withconventional power generation methods. A few applications of fusionreactors are now briefly discussed.

In some cases, fusion reactors may be used to retrofit a fossil fuelpower plant such as a power plant which burns coal, natural gas, orpetroleum to produce electricity. In some cases, fusion reactorsdescribed herein may be used to retrofit a fission power plant. Whenretrofitting a power plant, in some cases, it may only be necessary toreplace or update the portions of the power plant where energy isproduced. This makes power plant retrofits simple and cost efficient asturbines, generators, cooling towers, connections to a powerdistribution network, and other infrastructure may be reused. Forexample, a coal power plant may be retrofitted by replacing a coal-firedboiler with a fusion boiler that utilizes a reactor described herein.Similarly, a fission power plant may be retrofitted by replacing thecontrol rods and uranium fuel with a fusion reactor as described herein.

In some cases, a fusion reactor has a modular design that employs aplurality of smaller reactors. By having a plurality of reactors, thepower output of a plant may be modulated to meet energy demand byvarying the number of reactors in operation. Additionally, if individualreactors can be serviced or replaced while other reactors remainoperable, the overall power output of the plant may not be significantlyaffected.

In some cases, a fusion reactor may be used as a heating interface forindustrial processes such as fiberglass manufacture. In some cases, areactor is configured as the heat source for a steam generator (e.g., asteam generator used for steam cleaning or metal cutting). In somecases, a reactor is used as a source of helium where helium is producedas a result of a fusion reaction (e.g., when the reactor conductsproton-boron-11 fusion). In some cases, the reactor may be used as partof a water heater, such as a home-sized water heater. For example, thereactor may be placed within a water tank or may be thermally coupled toa water tank such that heat emanating from the reactor is used to heatwater. In some cases, a fusion-based water heater may be paired with awater radiator to provide indoor heating.

In some cases, a fusion reactor is used for transportation applications.For example, a fusion reactor may be used to power and automobiles,planes, trains, and boats. An automobile, for instance, may be outfittedwith a reactor having one or more energy conversion modules configuredto generate electrical and/or mechanical energy. In an electric car,electrical energy produced by a reactor may be used to charge a batteryor capacitor which is used to provide power to an electric motor. Forexample, a reactor may be operated to charge a car battery whenever thebattery's state of charge falls below a certain threshold value. In somecases, mechanical energy is produced by, for example, a Stirling enginewhich is used to provide the driving power for a car. In some cases, afusion reactor may be used to provide power to outer space vehicles.Some designs for outer space vehicles use a fission reactor such as aradioisotope thermoelectric generator. Such designs suffer from use andgeneration radioactive isotopes. They also require carrying relativelylarge amounts of radioactive fuel. Since reactors described herein maybe aneutronic or substantially aneutronic, these reactors may be muchmore preferable for spacecraft designed to carry human occupants.Additionally, the energy densities of fusion reactants used for reactorsdescribed herein are significantly higher than fuels required by afission reaction or a chemical reaction to produce the same amount ofenergy.

The claim elements that do not recite “means” or “step” are not in“means plus function” or “step plus function” form. (See, 35 USC §112(f)). Applicant intends that only claim elements reciting “means” or“step” be interpreted under or in accordance with 35 U.S.C. § 112(f).

The present disclosure may be embodied in other specific forms withoutdeparting from its spirit or essential characteristics. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive. The scope of the disclosure is, therefore,indicated by the appended claims rather than by the foregoingdescription. All changes which come within the meaning and range ofequivalency of the claims are to be embraced within their scope.

What is claimed is:
 1. An apparatus comprising: a confining wall havinga substantially cylindrical inner surface that has an axis, wherein theconfining wall at least partially encloses a confinement region; aplurality of electrodes azimuthally distributed along the confiningwall; an inlet to the confinement region for permitting introduction ofneutrals to the confinement region; at least one magnet configured toprovide a magnetic field in the confinement region such that themagnetic field is directed at least in part in the direction of the axisof the substantially cylindrical inner surface; a control systemcomprising a voltage and/or current source configured to (i)sequentially apply one or more potentials to each of the plurality ofelectrodes to induce and/or maintain rotational movement of ions and theneutrals in the confinement region, (ii) produce an electric field inthe confinement region directed at least in part in a radial directionwith respect to the substantially cylindrical inner surface, wherein theelectric field interacts with the magnetic field to induce and/ormaintain the rotational movement of ions and the neutrals in theconfinement region, and (iii) transition between (i) and (ii); and areactant attached to or embedded in the confining wall such that, duringoperation, repeated collisions between the neutrals and the reactantproduce an interaction with the reactant that gives off energy andproduces a product having a nuclear mass that is different from anuclear mass of any of the nuclei of the neutrals and the reactant. 2.The apparatus of claim 1, further comprising a first electrode formingat least a portion of the confining wall and a second electrode locatedwithin a region interior to the first electrode and separated from thefirst electrode by at least the confinement region, wherein the controlsystem is configured to produce the electric field in the confinementregion by applying a potential difference between the first electrodeand the second electrode.
 3. The apparatus of claim 1, furthercomprising: an inner wall within a region interior to the inner surfaceof the confining wall and separated from the confining wall by at leastthe confinement region; and a second plurality of electrodes azimuthallydistributed along the inner wall, wherein the control system is furtherconfigured to sequentially apply one or more potentials to each of thesecond plurality of electrodes.
 4. The apparatus of claim 3, wherein theinner wall is separated from the inner surface of the confining wall bya distance of, on average, about 1 mm to 50 cm.
 5. The apparatus ofclaim 1, wherein the plurality of electrodes includes at least fourelectrodes.
 6. The apparatus of claim 1, wherein the control system isconfigured to sequentially apply the one or more potentials to each ofthe plurality of electrodes according to a timing sequence that definesa speed of the rotational movement of the ions and the neutrals in theconfinement region.
 7. The apparatus of claim 1, wherein the confiningwall comprises a layered structure in which at least one the layerscomprises the plurality of electrodes azimuthally distributed along theconfining wall.
 8. The apparatus of claim 1, wherein the reactantattached to or embedded in the confining wall comprises boron-11, andwherein the neutrals comprise neutral hydrogen.
 9. The apparatus ofclaim 1, further comprising one or more electron emitters configured to,during operation, emit electrons into a region adjacent to the confiningwall.
 10. The apparatus of claim 9, wherein the one or more electronemitters comprise boron or a boron-containing material.
 11. Theapparatus of claim 1, wherein the plurality of electrodes, the at leastone magnet, and/or the control system are further configured to inducerotational movement of the neutrals in the confinement region at anaverage velocity of at least about 50,000 m/s.
 12. An apparatuscomprising: a confining wall having a substantially cylindrical innersurface that has an axis, wherein the confining wall at least partiallyencloses a confinement region; a plurality of electrodes azimuthallydistributed along the confining wall; an inlet to the confinement regionfor permitting introduction of neutrals to the confinement region; atleast one magnet configured to provide a magnetic field in theconfinement region such that the magnetic field is directed at least inpart in a radial direction with respect to the substantially cylindricalinner surface; a control system comprising a voltage and/or currentsource configured to (i) sequentially apply one or more potentials toeach of the plurality of electrodes to induce and/or maintain rotationalmovement of ions and the neutrals in the confinement region, (ii) applya potential difference between two of the plurality of electrodes toproduce an electric field in the confinement region such that theelectric field is directed at least in part in an axial direction withrespect to the substantially cylindrical inner surface, wherein theelectric field interacts with the magnetic field to induce and/ormaintain the rotational movement of ions and the neutrals in theconfinement region, and (iii) transition between (i) and (ii); and areactant attached to or embedded in the confining wall such that, duringoperation, repeated collisions between the neutrals and the reactantproduce an interaction with the reactant that gives off energy andproduces a product having a nuclear mass that is different from anuclear mass of any of the nuclei of the neutrals and the reactant. 13.The apparatus of claim 12, wherein the at least one magnet comprises: afirst ring magnet defining or disposed on at least part of the confiningwall; and a second ring magnet located within a region interior to andsubstantially concentric with the first ring magnet, wherein the secondring magnet is separated from the from the first ring magnet by at leastthe confinement region.
 14. The apparatus of claim 12, wherein theplurality of electrodes comprises a first set of electrodes azimuthallydistributed along the confining wall on a first axial side of theconfining wall and a second set of electrodes azimuthally distributedalong the confining wall on a second axial side of the confining wall,opposite the first axial side of the confining wall, wherein the controlsystem is configured to apply the potential difference between at leastone electrode of the first set of electrodes and at least one electrodeof the second set of electrodes.
 15. The apparatus of claim 14, whereinthe control system is configured to: (a) apply the potential differencebetween all or a substantial fraction of the electrodes in the first setof electrodes and all or a substantial fraction of the electrodes in thesecond set of electrodes at the same time to produce the electric fieldin the confinement region that is directed at least in part in an axialdirection with respect to the substantially cylindrical inner surface;and (b) after (a), sequentially apply the one or more potentials to eachof the plurality of electrodes in an azimuthally sequential manner tomaintain the rotational movement of the ions and neutrals in theconfinement region.
 16. A method of operating a reactor comprising: aconfining wall having a substantially cylindrical inner surface that hasan axis, wherein the confining wall at least partially encloses aconfinement region; a plurality of electrodes azimuthally distributedalong the confining wall; an inlet to the confinement region forpermitting introduction of neutrals to the confinement region; at leastone magnet configured to provide a magnetic field in the confinementregion such that the magnetic field is directed at least in part in thedirection of the axis of the substantially cylindrical inner surface;and a reactant attached to or embedded in the confining wall, the methodcomprising: (i) sequentially applying one or more potentials to each ofthe plurality of electrodes azimuthally distributed along the confiningwall to induce and/or maintain rotational movement of ions and neutralsin the confinement region; (ii) producing an electric field in theconfinement region directed at least in part in a radial direction withrespect to the substantially cylindrical inner surface, wherein theelectric field interacts with the magnetic field to induce and/ormaintain the rotational movement of ions and the neutrals in theconfinement region; and (iii) transitioning between (i) and (ii),wherein repeated collisions between the neutrals and the reactantproduce an interaction with the reactant that gives off energy andproduces a product having a nuclear mass that is different from anuclear mass of any of the nuclei of the neutrals and the reactant. 17.The method of claim 16, wherein the reactor further comprises a firstelectrode forming at least a portion of the confining wall and a secondelectrode located within a region interior to the first electrode andseparated from the first electrode by at least the confinement region,and wherein producing the electric field in the confinement regioncomprises applying a potential difference between the first electrodeand the second electrode.
 18. The method of claim 16, wherein thereactor further comprises: an inner wall within a region interior to theinner surface of the confining wall and separated from the confiningwall by at least the confinement region; and a second plurality ofelectrodes azimuthally distributed along the inner wall, wherein themethod further comprises sequentially applying one or more potentials toeach of the second plurality of electrodes.
 19. The method of claim 16,wherein sequentially applying one or more potentials to each of theplurality of electrodes comprises applying the one or more potentialsaccording to a timing sequence that defines a speed of the rotationalmovement of the ions and the neutrals in the confinement region.
 20. Themethod of claim 16, wherein the interaction is a fusion reaction. 21.The method of claim 20, wherein the fusion reaction is aneutronic. 22.The method of claim 16, wherein the reactant attached to or embedded inthe confining wall comprises boron-11, and wherein the neutrals compriseneutral hydrogen.
 23. The method of claim 16, further comprisingproducing an electron rich region having an excess of electrons overpositively charged particles of at least about 10⁶/cm³, wherein theelectron rich region is proximate the confining wall the confinementregion.
 24. The method of claim 23, wherein the electron rich region hasan electric field strength of at least about 10⁶ V/m.
 25. The method ofclaim 23, wherein the neutrals in the electron rich region have anenergy of, on average, of between about 0.1 eV and 2 eV.
 26. The methodof claim 16, further comprising controlling the magnetic field in theconfinement region.
 27. The method of claim 16, further comprisingcontrolling a supply of neutrals to the confinement region via theinlet.
 28. The method of claim 16, wherein the induced and/or maintainedrotational movement of ions and the neutrals in the confinement regionprovides the ions and neutrals with an average velocity of at leastabout 50,000 m/s.
 29. A method of operating a reactor comprising: aconfining wall having a substantially cylindrical inner surface that hasan axis, wherein the confining wall at least partially encloses aconfinement region; a plurality of electrodes azimuthally distributedalong the confining wall; an inlet to the confinement region forpermitting introduction of neutrals to the confinement region; at leastone magnet configured to provide a magnetic field in the confinementregion such that the magnetic field is directed at least in part in aradial direction with respect the substantially cylindrical innersurface; and a reactant attached to or embedded in the confining wall,the method comprising: (i) sequentially applying one or more potentialsto each of the plurality of electrodes azimuthally distributed along theconfining wall to induce and/or maintain rotational movement of ions andneutrals in the confinement region; (ii) applying a potential differencebetween two of the plurality of electrodes to produce an electric fieldin the confinement region such that the electric field is directed atleast in part in an axial direction with respect to the substantiallycylindrical inner surface, wherein the electric field interacts with themagnetic field to induce and/or maintain the rotational movement of ionsand the neutrals in the confinement region; and (iii) transitioningbetween (i) and (ii), wherein repeated collisions between the neutralsand the reactant produce an interaction with the reactant that gives offenergy and produces a product having a nuclear mass that is differentfrom a nuclear mass of any of the nuclei of the neutrals and thereactant.
 31. The method of claim 29, wherein the plurality ofelectrodes comprises a first set of electrodes azimuthally distributedalong the confining wall on a first axial side of the confining wall anda second set of electrodes azimuthally distributed along the confiningwall on a second axial side of the confining wall, opposite the firstaxial side of the confining wall, and wherein the method furthercomprises applying the potential difference between at least oneelectrode of the first set of electrodes and at least one electrode ofthe second set of electrodes.